# Ethiopian multiplication

Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving.

Ethiopian multiplication
You are encouraged to solve this task according to the task description, using any language you may know.

Method:

1. Take two numbers to be multiplied and write them down at the top of two columns.
2. In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last in the same column, until you write a value of 1.
3. In the right-hand column repeatedly double the last number and write the result below. stop when you add a result in the same row as where the left hand column shows 1.
4. Examine the table produced and discard any row where the value in the left column is even.
5. Sum the values in the right-hand column that remain to produce the result of multiplying the original two numbers together

For example:   17 × 34

       17    34


Halving the first column:

       17    34
8
4
2
1


Doubling the second column:

       17    34
8    68
4   136
2   272
1   544


Strike-out rows whose first cell is even:

       17    34
8    68
4   136
2   272
1   544


Sum the remaining numbers in the right-hand column:

       17    34
8    --
4   ---
2   ---
1   544
====
578


So 17 multiplied by 34, by the Ethiopian method is 578.

The task is to define three named functions/methods/procedures/subroutines:

1. one to halve an integer,
2. one to double an integer, and
3. one to state if an integer is even.

Use these functions to create a function that does Ethiopian multiplication.

References

## 11l

Translation of: Python
F halve(x)
R x I/ 2

F double(x)
R x * 2

F even(x)
R !(x % 2)

F ethiopian(=multiplier, =multiplicand)
V result = 0

L multiplier >= 1
I !even(multiplier)
result += multiplicand
multiplier = halve(multiplier)
multiplicand = double(multiplicand)

R result

print(ethiopian(17, 34))
Output:
578

## 8080 Assembly

The 8080 does not have a hardware multiplier, but it does have addition and rotation, so this code is actually useful. Indeed, it is pretty much the standard algorithm for general multiplication on processors that do not have a hardware multiplier.

You would not normally name the sections (halve, double, even), since they rely on each other and cannot be called independently. Pulling them out entirely would entail a performance hit and make the whole thing much less elegant, so I've done it this way as a sort of compromise.

	org	100h
jmp	demo
;;;	HL = BC * DE
;;;	BC is left column, DE is right column
emul:	lxi	h,0	; HL will be the accumulator

ztest:	mov	a,b	; Check if the left column is zero.
ora	c	; If so, stop.
rz

halve:	mov	a,b	; Halve BC by rotating it right.
rar		; We know the carry is zero here because of the ORA.
mov	b,a	; So rotate the top half first,
mov	a,c	; Then the bottom half
rar		; This leaves the old low bit in the carry flag,
mov	c,a	; so this also lets us do the even/odd test in one go.

even:	jnc	$+4 ; If no carry, the number is even, so skip (strikethrough) dad d ; But if odd, add the number in the right column double: xchg ; Doubling DE is a bit easier since you can add dad h ; HL to itself in one go, and XCHG swaps DE and HL xchg jmp ztest ; We want to do the whole thing again until BC is zero ;;; Demo code, print 17 * 34 demo: lxi b,17 ; Load 17 into BC (left column) lxi d,34 ; Load 34 into DE (right column) call emul ; Do the multiplication print: lxi b,-10 ; Decimal output routine (not very interesting here, lxi d,pbuf ; but without it you can't see the result) push d digit: lxi d,-1 dloop: inx d dad b jc dloop mvi a,58 add l pop h dcx h mov m,a push h xchg mov a,h ora l jnz digit pop d mvi c,9 jmp 5 db '*****' pbuf: db '$'
Output:
578

## AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits
or android 64 bits with application Termux
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program multieth64.s   */

/************************************/
/* Constantes                       */
/************************************/
.include "../includeConstantesARM64.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessResult:         .asciz "Result : "
szMessStart:          .asciz "Program 64 bits start.\n"
szCarriageReturn:     .asciz "\n"
szMessErreur:         .asciz "Error overflow. \n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:             .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                            // entry of program
bl affichageMess
mov x0,#17
mov x1,#34
bl multEthiop
bl conversion10              // decimal conversion
mov x0,#3                    // number string to display
ldr x2,qAdrsZoneConv         // insert conversion in message
bl displayStrings            // display message

100:                              // standard end of the program
mov x0, #0                    // return code
mov x8,EXIT
svc #0                        // perform the system call
/******************************************************************/
/*     Ethiopian multiplication   unsigned                        */
/******************************************************************/
/*  x0  first factor */
/*  x1   2th  factor  */
/*  x0 return résult  */
multEthiop:
stp x1,lr,[sp,-16]!        // save  registers
stp x2,x3,[sp,-16]!        // save  registers
mov x2,#0                  // init result
1:                            // loop
cmp x0,#1                  // end ?
blt 3f
ands x3,x0,#1              //
add x3,x2,x1               // add factor2 to result
csel x2,x2,x3,eq
mov x3,1
lsr x0,x0,x3               // divide factor1 by 2
cmp x1,0                  // overflow ? if bit 63 = 1 ie negative number
blt 2f
mov x4,1
lsl x1,x1,x4               // multiply factor2 by 2
b 1b                       // or loop
2:                            // error display
bl affichageMess
mov x2,#0
3:
mov x0,x2                  // return result
ldp x2,x3,[sp],16          // restaur  registers
ldp x1,lr,[sp],16          // restaur  registers
ret
/***************************************************/
/*   display multi strings                    */
/***************************************************/
/* x0  contains number strings address */
/* x1 address string1 */
/* x2 address string2 */
/* x3 address string3 */
/* other address on the stack */
/* thinck to add  number other address * 8 to add to the stack */
displayStrings:            // INFO:  displayStrings
stp x1,lr,[sp,-16]!    // save  registers
stp x2,x3,[sp,-16]!    // save  registers
stp x4,x5,[sp,-16]!    // save  registers
add fp,sp,#48          // save paraméters address (6 registers saved * 4 bytes)
mov x4,x0              // save strings number
cmp x4,#0              // 0 string -> end
ble 100f
mov x0,x1              // string 1
bl affichageMess
cmp x4,#1              // number > 1
ble 100f
mov x0,x2
bl affichageMess
cmp x4,#2
ble 100f
mov x0,x3
bl affichageMess
cmp x4,#3
ble 100f
mov x3,#3
sub x2,x4,#8
1:                         // loop extract address string on stack
ldr x0,[fp,x2,lsl #3]
bl affichageMess
subs x2,x2,#1
bge 1b
100:
ldp x4,x5,[sp],16      // restaur  registers
ldp x2,x3,[sp],16      // restaur  registers
ldp x1,lr,[sp],16      // restaur  registers
ret

/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../includeARM64.inc"
Output:
Program 64 bits start.
Result : 578


## ACL2

(include-book "arithmetic-3/top" :dir :system)

(defun halve (x)
(floor x 2))

(defun double (x)
(* x 2))

(defun is-even (x)
(evenp x))

(defun multiply (x y)
(if (zp (1- x))
y
(+ (if (is-even x)
0
y)
(multiply (halve x) (double y)))))


## Action!

INT FUNC EthopianMult(INT a,b)
INT res

PrintF("Ethopian multiplication %I by %I:%E",a,b)
res=0
WHILE a>=1
DO
IF a MOD 2=0 THEN
PrintF("%I %I strike%E",a,b)
ELSE
PrintF("%I %I keep%E",a,b)
res==+b
FI
a==/2
b==*2
OD
RETURN (res)

PROC Main()
INT res

res=EthopianMult(17,34)
PrintF("Result is %I",res)
RETURN
Output:
Ethopian multiplication 17 by 34:
17 34 keep
8 68 strike
4 136 strike
2 272 strike
1 544 keep
Result is 578


## ActionScript

Works with: ActionScript version 2.0
function Divide(a:Number):Number {
return ((a-(a%2))/2);
}
function Multiply(a:Number):Number {
return (a *= 2);
}
function isEven(a:Number):Boolean {
if (a%2 == 0) {
return (true);
} else {
return (false);
}
}
function Ethiopian(left:Number, right:Number) {
var r:Number = 0;
trace(left+"     "+right);
while (left != 1) {
var State:String = "Keep";
if (isEven(Divide(left))) {
State = "Strike";
}
trace(Divide(left)+"     "+Multiply(right)+"  "+State);
left = Divide(left);
right = Multiply(right);
if (State == "Keep") {
r += right;
}
}
trace("="+"      "+r);
}
}

Output:

ex. Ethiopian(17,34);

17     34
8     68  Strike
4     136  Strike
2     272  Strike
1     544  Keep


with ada.text_io;use ada.text_io;

procedure ethiopian is
function double  (n : Natural) return Natural is (2*n);
function halve   (n : Natural) return Natural is (n/2);
function is_even (n : Natural) return Boolean is (n mod 2 = 0);

function mul (l, r : Natural) return Natural is
(if l = 0 then 0 elsif l = 1 then r elsif is_even (l) then mul (halve (l),double (r))
else r + double (mul (halve (l), r)));

begin
put_line (mul (17,34)'img);
end ethiopian;


## Aime

Translation of: C
void
halve(integer &x)
{
x >>= 1;
}

void
double(integer &x)
{
x <<= 1;
}

integer
iseven(integer x)
{
return (x & 1) == 0;
}

integer
ethiopian(integer plier, integer plicand, integer tutor)
{
integer result;

result = 0;

if (tutor) {
o_form("ethiopian multiplication of ~ by ~\n", plier, plicand);
}

while (plier >= 1) {
if (iseven(plier)) {
if (tutor) {
o_form("/w4/ /w6/ struck\n", plier, plicand);
}
} else {
if (tutor) {
o_form("/w4/ /w6/ kept\n", plier, plicand);
}

result += plicand;
}

halve(plier);
double(plicand);
}

return result;
}

integer
main(void)
{
o_integer(ethiopian(17, 34, 1));
o_byte('\n');

return 0;
}
 17     34 kept
8     68 struck
4    136 struck
2    272 struck
1    544 kept
578


## ALGOL 68

Translation of: C
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
PROC halve = (REF INT x)VOID: x := ABS(BIN x SHR 1);
PROC doublit = (REF INT x)VOID: x := ABS(BIN x SHL 1);
PROC iseven = (#CONST# INT x)BOOL: NOT ODD x;

PROC ethiopian = (INT in plier,
INT in plicand, #CONST# BOOL tutor)INT:
(
INT plier := in plier, plicand := in plicand;
INT result:=0;

IF tutor THEN
printf(($"ethiopian multiplication of "g(0)," by "g(0)l$, plier, plicand)) FI;

WHILE plier >= 1 DO
IF iseven(plier) THEN
IF tutor THEN printf(($" "4d," "6d" struck"l$, plier, plicand)) FI
ELSE
IF tutor THEN printf(($" "4d," "6d" kept"l$, plier, plicand)) FI;
result +:= plicand
FI;
halve(plier); doublit(plicand)
OD;
result
);

main:
(
printf(($g(0)l$, ethiopian(17, 34, TRUE)))
)
Output:
ethiopian multiplication of 17 by 34
0017  000034 kept
0008  000068 struck
0004  000136 struck
0002  000272 struck
0001  000544 kept
578


## ALGOL-M

BEGIN

INTEGER FUNCTION HALF(I);
INTEGER I;
BEGIN
HALF := I / 2;
END;

INTEGER FUNCTION DOUBLE(I);
INTEGER I;
BEGIN
DOUBLE := I + I;
END;

% RETURN 1 IF EVEN, OTHERWISE 0 %
INTEGER FUNCTION EVEN(I);
INTEGER I;
BEGIN
EVEN := 1 - (I - 2 * (I / 2));
END;

% RETURN I * J AND OPTIONALLY SHOW COMPUTATIONAL STEPS %
INTEGER FUNCTION ETHIOPIAN(I, J, SHOW);
INTEGER I, J, SHOW;
BEGIN
INTEGER P, YES;
YES := 1;
P := 0;
WHILE I >= 1 DO
BEGIN
IF EVEN(I) = YES THEN
BEGIN
IF SHOW = YES THEN WRITE(I,"  ----", J);
END
ELSE
BEGIN
IF SHOW = YES THEN WRITE(I,J);
P := P + J;
END;
I := HALF(I);
J := DOUBLE(J);
END;
IF SHOW = YES THEN WRITE("     =");
ETHIOPIAN := P;
END;

% EXERCISE THE FUNCTION %
INTEGER YES;
YES := 1;
WRITE(ETHIOPIAN(17,34,YES));

END
Output:
    17   34
8 ----   68
4 ----  136
2 ----  272
1  544
=  578


## ALGOL W

begin
% returns half of a %
integer procedure halve  ( integer value a ) ; a div 2;
% returns a doubled %
integer procedure double ( integer value a ) ; a * 2;
% returns true if a is even, false otherwise %
logical procedure even   ( integer value a ) ; not odd( a );
% returns the product of a and b using ethopian multiplication %
% rather than keep a table of the intermediate results,        %
% we examine then as they are generated                        %
integer procedure ethopianMultiplication ( integer value a, b ) ;
begin
integer v, r, accumulator;
v           := a;
r           := b;
accumulator := 0;
i_w := 4; s_w := 0; % set output formatting %
while begin
write( v );
if even( v ) then writeon( "    ---" )
else begin
accumulator := accumulator + r;
writeon( "   ", r );
end;
v := halve( v );
r := double( r );
v > 0
end do begin end;
write( "      =====" );
accumulator
end ethopianMultiplication ;
% task test case %
begin
integer m;
m := ethopianMultiplication( 17, 34 );
write( "       ", m )
end
end.
Output:
  17     34
8    ---
4    ---
2    ---
1    544
=====
578


## AppleScript

Translation of: JavaScript

Note that this algorithm, already described in the Rhind Papyrus (c. BCE 1650), can be used to multiply strings as well as integers, if we change the identity element from 0 to the empty string, and replace integer addition with string concatenation.

on run
{ethMult(17, 34), ethMult("Rhind", 9)}

--> {578, "RhindRhindRhindRhindRhindRhindRhindRhind"}
end run

-- Int -> Int -> Int
-- or
-- Int -> String -> String
on ethMult(m, n)
script fns
property identity : missing value
property plus : missing value

on half(n) -- 1. half an integer (div 2)
n div 2
end half

on double(n) -- 2. double (add to self)
plus(n, n)
end double

on isEven(n) -- 3. is n even ? (mod 2 > 0)
(n mod 2) > 0
end isEven

on chooseFns(c)
if c is string then
set identity of fns to ""
set plus of fns to plusString of fns
else
set identity of fns to 0
set plus of fns to plusInteger of fns
end if
end chooseFns

on plusInteger(a, b)
a + b
end plusInteger

on plusString(a, b)
a & b
end plusString
end script

chooseFns(class of m) of fns

-- MAIN PROCESS OF CALCULATION

set o to identity of fns
if n < 1 then return o

repeat while (n > 1)
if isEven(n) of fns then -- 3. is n even ? (mod 2 > 0)
set o to plus(o, m) of fns
end if
set n to half(n) of fns -- 1. half an integer (div 2)
set m to double(m) of fns -- 2. double  (add to self)
end repeat
return plus(o, m) of fns
end ethMult

Output:
{578, "RhindRhindRhindRhindRhindRhindRhindRhindRhind"}

## ARM Assembly

Works with: as version Raspberry Pi
or android 32 bits with application Termux
/* ARM assembly Raspberry PI  */
/*  program multieth.s   */

/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly
for the routine affichageMess conversion10
see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessResult:         .asciz "Result : "
szMessStart:          .asciz "Program 32 bits start.\n"
szCarriageReturn:     .asciz "\n"
szMessErreur:         .asciz "Error overflow. \n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:             .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main
main:                            @ entry of program
bl affichageMess
mov r0,#17
mov r1,#34
bl multEthiop
bl conversion10              @ decimal conversion
mov r0,#3                    @ number string to display
ldr r2,iAdrsZoneConv         @ insert conversion in message
bl displayStrings            @ display message

100:                              @ standard end of the program
mov r0, #0                    @ return code
mov r7, #EXIT                 @ request to exit program
svc #0                        @ perform the system call
/******************************************************************/
/*     Ethiopian multiplication                                  */
/******************************************************************/
/*  r0  first factor */
/*  r1   2th  factor  */
/*  r0 return résult  */
multEthiop:
push {r1-r3,lr}            @ save registers
mov r2,#0                  @ init result
1:                            @ loop
cmp r0,#1                  @ end ?
blt 3f
ands r3,r0,#1              @
addne r2,r1                @ add factor2 to result
lsr r0,#1                  @ divide factor1 by 2
lsls r1,#1                 @ multiply factor2 by 2
bcs 2f                     @ overflow ?
b 1b                       @ or loop
2:                            @ error display
bl affichageMess
mov r2,#0
3:
mov r0,r2                  @ return result
pop {r1-r3,pc}
/***************************************************/
/*   display multi strings                    */
/***************************************************/
/* r0  contains number strings address */
/* r1 address string1 */
/* r2 address string2 */
/* r3 address string3 */
/* other address on the stack */
/* thinck to add  number other address * 4 to add to the stack */
displayStrings:            @ INFO:  displayStrings
push {r1-r4,fp,lr}     @ save des registres
add fp,sp,#24          @ save paraméters address (6 registers saved * 4 bytes)
mov r4,r0              @ save strings number
cmp r4,#0              @ 0 string -> end
ble 100f
mov r0,r1              @ string 1
bl affichageMess
cmp r4,#1              @ number > 1
ble 100f
mov r0,r2
bl affichageMess
cmp r4,#2
ble 100f
mov r0,r3
bl affichageMess
cmp r4,#3
ble 100f
mov r3,#3
sub r2,r4,#4
1:                         @ loop extract address string on stack
ldr r0,[fp,r2,lsl #2]
bl affichageMess
subs r2,#1
bge 1b
100:
pop {r1-r4,fp,pc}

/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
Output:
Program 32 bits start.
Result : 578


## Arturo

halve: function [x]-> shr x 1
double: function [x]-> shl x 1

; even? already exists

ethiopian: function [x y][
prod: 0
while [x > 0][
unless even? x [prod: prod + y]
x: halve x
y: double y
]
return prod
]

print ethiopian 17 34
print ethiopian 2 3

Output:
578
6

## AutoHotkey

MsgBox % Ethiopian(17, 34) "n" Ethiopian2(17, 34)

; func definitions:
half( x ) {
return x >> 1
}

double( x ) {
return x << 1
}

isEven( x ) {
return x & 1 == 0
}

Ethiopian( a, b ) {
r := 0
While (a >= 1) {
if !isEven(a)
r += b
a := half(a)
b := double(b)
}
return r
}

; or a recursive function:
Ethiopian2( a, b, r = 0 ) { ;omit r param on initial call
return a==1 ? r+b : Ethiopian2( half(a), double(b), !isEven(a) ? r+b : r )
}


## AutoIt

Func Halve($x) Return Int($x/2)
EndFunc

Func Double($x) Return ($x*2)
EndFunc

Func IsEven($x) Return (Mod($x,2) == 0)
EndFunc

; this version also supports negative parameters
Func Ethiopian($nPlier,$nPlicand, $bTutor = True) Local$nResult = 0
If ($nPlier < 0) Then$nPlier =- $nPlier$nPlicand =- $nPlicand ElseIf ($nPlicand > 0) And ($nPlier >$nPlicand) Then
$nPlier =$nPlicand
$nPlicand =$nPlier
EndIf
If $bTutor Then _ ConsoleWrite(StringFormat("Ethiopian multiplication of %d by %d...\n",$nPlier, $nPlicand)) While ($nPlier >= 1)
If Not IsEven($nPlier) Then$nResult += $nPlicand If$bTutor Then ConsoleWrite(StringFormat("%d\t%d\tKeep\n", $nPlier,$nPlicand))
Else
If $bTutor Then ConsoleWrite(StringFormat("%d\t%d\tStrike\n",$nPlier, $nPlicand)) EndIf$nPlier = Halve($nPlier)$nPlicand = Double($nPlicand) WEnd If$bTutor Then ConsoleWrite(StringFormat("Answer = %d\n", $nResult)) Return$nResult
EndFunc

MsgBox(0, "Ethiopian multiplication of 17 by 34", Ethiopian(17, 34) )


## AWK

Implemented without the tutor.

function halve(x)
{
return int(x/2)
}

function double(x)
{
return x*2
}

function iseven(x)
{
return x%2 == 0
}

function ethiopian(plier, plicand)
{
r = 0
while(plier >= 1) {
if ( !iseven(plier) ) {
r += plicand
}
plier = halve(plier)
plicand = double(plicand)
}
return r
}

BEGIN {
print ethiopian(17, 34)
}


## BASIC

### Applesoft BASIC

Same code as Nascom BASIC

### ASIC

REM Ethiopian multiplication
X = 17
Y = 34
TOT = 0
WHILE X >= 1
PRINT X;
PRINT " ";
A = X
GOSUB CHECKEVEN:
IF ISEVEN = 0 THEN
TOT = TOT + Y
PRINT Y;
ENDIF
PRINT
A = X
GOSUB HALVE:
X = A
A = Y
GOSUB DOUBLE:
Y = A
WEND
PRINT "=      ";
PRINT TOT
END

REM Subroutines are required, though
REM they complicate the code

DOUBLE:
A = 2 * A
RETURN

HALVE:
A = A / 2
RETURN

CHECKEVEN:
REM ISEVEN - result (0 if A odd, 1 otherwise)
ISEVEN = A MOD 2
ISEVEN = 1 - ISEVEN
RETURN

Output:
    17     34
8
4
2
1    544
=         578


### BASIC

Works with QBasic. While building the table, it's easier to simply not print unused values, rather than have to go back and strike them out afterward. (Both that and the actual adding happen in the "IF NOT (isEven(x))" block.)

DECLARE FUNCTION half% (a AS INTEGER)
DECLARE FUNCTION doub% (a AS INTEGER)
DECLARE FUNCTION isEven% (a AS INTEGER)

DIM x AS INTEGER, y AS INTEGER, outP AS INTEGER

x = 17
y = 34

DO
PRINT x,
IF NOT (isEven(x)) THEN
outP = outP + y
PRINT y
ELSE
PRINT
END IF
IF x < 2 THEN EXIT DO
x = half(x)
y = doub(y)
LOOP

PRINT " =", outP

FUNCTION doub% (a AS INTEGER)
doub% = a * 2
END FUNCTION

FUNCTION half% (a AS INTEGER)
half% = a \ 2
END FUNCTION

FUNCTION isEven% (a AS INTEGER)
isEven% = (a MOD 2) - 1
END FUNCTION

Output:
 17            34
8
4
2
1             544
=             578

### BASIC256

outP = 0
x = 17
y = 34

while True
print x + chr(09);
if not (isEven(x)) then
outP += y
print y
else
print
end if
if x < 2 then exit while
x = half(x)
y = doub(y)
end while
print "=" + chr(09); outP
end

function doub (a)
return a * 2
end function

function half (a)
return a \ 2
end function

function isEven (a)
return (a mod 2) - 1
end function


### BBC BASIC

      x% = 17
y% = 34

REPEAT
IF NOT FNeven(x%) THEN
p% += y%
PRINT x%, y%
ELSE
PRINT x%, "       ---"
ENDIF
x% = FNhalve(x%)
y% = FNdouble(y%)
UNTIL x% = 0
PRINT " " , "       ==="
PRINT " " , p%
END

DEF FNdouble(A%) = A% * 2

DEF FNhalve(A%) = A% DIV 2

DEF FNeven(A%) = ((A% AND 1) = 0)

Output:
        17        34
8       ---
4       ---
2       ---
1       544
===
578

### Chipmunk Basic

Translation of: BASIC256
Works with: Chipmunk Basic version 3.6.4
100 sub doub(a)
110 doub = a*2
120 end sub
130 sub half(a)
140 half = int(a/2)
150 end sub
160 sub iseven(a)
170 iseven = (a mod 2)-1
180 end sub
190 outp = 0
200 x = 17
210 y = 34
220 while 1
230   print x;chr$(9); 240 if not (iseven(x)) then 250 outp = outp - y 260 print y 270 else 280 print 290 endif 300 if x < 2 then exit while 310 x = half(x) 320 y = doub(y) 330 wend 340 print "=";chr$(9);outp
350 end


### FreeBASIC

Function double_(y As String) As String
For n_ As Integer=Len(y)-1 To 0 Step -1
Next n_
End Function

Function Accumulate(NUM1 As String,NUM2 As String) As String
Var three="0"+NUM1
Var two=String(len(NUM1)-len(NUM2),"0")+NUM2
For n2 As Integer=len(NUM1)-1 To 0 Step -1
Next n2
three=Ltrim(three,"0")
If three="" Then Return "0"
Return three
End Function

Function Half(Byref x As String) As String
Var carry=0
For z As Integer=0 To Len(x)-1
Var temp=(x[z]-48+carry)
Var main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
x[z]=main+48
Next z
x= Ltrim(x,"0")
Return x
End Function

Function IsEven(x As String) As Integer
If x[Len(x)-1] And 1  Then Return 0
return -1
End Function

Function EthiopianMultiply(n1 As String,n2 As String) As String
Dim As String x=n1,y=n2
If Len(y)>Len(x) Then Swap y,x
'set the largest one to be halfed
If Len(y)=Len(x) Then
If x<y Then Swap y,x
End If
Dim As String ans
Dim As String temprint,odd
While x<>""
temprint=""
odd=""
If  not IsEven(x) Then
temprint=" *"
odd=" <-- odd"
ans=Accumulate(y,ans)
End If
Print x;odd;tab(30);y;temprint
x=Half(x)
y= Double_(y)
Wend
Return ans
End Function
'=================  Example ====================
Print
Dim As String s1="17"
Dim As String s2="34"
Print "Half";tab(30);"Double     * marks those accumulated"
print "Biggest";tab(30);"Smallest"

Print

Var ans= EthiopianMultiply(s1,s2)

Print
Print
Print " ";ans
print "Float check"
Print Val(s1)*Val(s2)

Sleep
note: algorithm uses strings instead of integers
Output:
Half                         Double     * marks those accumulated
Biggest                      Smallest

34                           17
17 <-- odd                   34 *
8                            68
4                            136
2                            272
1 <-- odd                    544 *

578
Float check
578

### GW-BASIC

Works with: BASICA
10  REM Ethiopian multiplication
20  DEF FNE(A%) = (A% + 1) MOD 2
30  DEF FNH(A%) = A% \ 2
40  DEF FND(A%) = 2 * A%
50  X% = 17: Y% = 34: TOT% = 0
60  WHILE X% >= 1
70   PRINT USING "###### "; X%;
80   IF FNE(X%)=0 THEN TOT% = TOT% + Y%: PRINT USING "###### "; Y% ELSE PRINT
90   X% = FNH(X%): Y% = FND(Y%)
100 WEND
110 PRINT USING "=      ######"; TOT%
120 END
Output:
    17     34
8
4
2
1    544
=         578


### Liberty BASIC

x = 17
y = 34
msg$= str$(x) + " * " + str$(y) + " = " Print str$(x) + "    " + str$(y) 'In this routine we will not worry about discarding the right hand value whos left hand partner is even; 'we will just not add it to our product. Do Until x < 2 If Not(isEven(x)) Then product = (product + y) End If x = halveInt(x) y = doubleInt(y) Print str$(x) + "    " + str$(y) Loop product = (product + y) If (x < 0) Then product = (product * -1) Print msg$ + str$(product) Function isEven(num) isEven = Abs(Not(num Mod 2)) End Function Function halveInt(num) halveInt = Int(num/ 2) End Function Function doubleInt(num) doubleInt = Int(num * 2) End Function ### Microsoft Small Basic x = 17 y = 34 tot = 0 While x >= 1 TextWindow.Write(x) TextWindow.CursorLeft = 10 If Math.Remainder(x + 1, 2) = 0 Then tot = tot + y TextWindow.WriteLine(y) Else TextWindow.WriteLine("") EndIf x = Math.Floor(x / 2) y = 2 * y EndWhile TextWindow.Write("=") TextWindow.CursorLeft = 10 TextWindow.WriteLine(tot) ### Minimal BASIC 10 REM Ethiopian multiplication 20 DEF FND(A) = 2*A 30 DEF FNH(A) = INT(A/2) 40 DEF FNE(A) = A-INT(A/2)*2-1 50 LET X = 17 60 LET Y = 34 70 LET T = 0 80 IF X < 1 THEN 170 90 IF FNE(X) <> 0 THEN 130 100 LET T = T+Y 110 PRINT X; TAB(9); Y; "(kept)" 120 GOTO 140 130 PRINT X; TAB(9); Y 140 LET X = FNH(X) 150 LET Y = FND(Y) 160 GOTO 80 170 PRINT "------------" 180 PRINT "= "; TAB(9); T; "(sum of kept second vals)" 190 END ### MSX Basic Works with: MSX BASIC version any Same code as Nascom BASIC ### Nascom BASIC Translation of: Modula-2 Works with: Nascom ROM BASIC version 4.7 10 REM Ethiopian multiplication 20 DEF FND(A)=2*A 30 DEF FNH(A)=INT(A/2) 40 DEF FNE(A)=A-INT(A/2)*2-1 50 X=17 60 Y=34 70 TT=0 80 IF X<1 THEN 150 90 NR=X:GOSUB 1000:PRINT " "; 100 IF FNE(X)=0 THEN TT=TT+Y:NR=Y:GOSUB 1000 110 PRINT 120 X=FNH(X) 130 Y=FND(Y) 140 GOTO 80 150 PRINT "= "; 160 NR=TT:GOSUB 1000:PRINT 170 END 995 REM Print NR in 9 fields 1000 S$=STR$(NR) 1010 PRINT SPC(9-LEN(S$));S$; 1020 RETURN  Output:  17 34 8 4 2 1 544 = 578 ### PureBasic Procedure isEven(x) ProcedureReturn (x & 1) ! 1 EndProcedure Procedure halveValue(x) ProcedureReturn x / 2 EndProcedure Procedure doubleValue(x) ProcedureReturn x << 1 EndProcedure Procedure EthiopianMultiply(x, y) Protected sum Print("Ethiopian multiplication of " + Str(x) + " and " + Str(y) + " ... ") Repeat If Not isEven(x) sum + y EndIf x = halveValue(x) y = doubleValue(y) Until x < 1 PrintN(" equals " + Str(sum)) ProcedureReturn sum EndProcedure If OpenConsole() EthiopianMultiply(17,34) Print(#CRLF$ + #CRLF$+ "Press ENTER to exit") Input() CloseConsole() EndIf Output: Ethiopian multiplication of 17 and 34 ... equals 578  It became apparent that according to the way the Ethiopian method is described above it can't produce a correct result if the first multiplicand (the one being repeatedly halved) is negative. I've addressed that in this variation. If the first multiplicand is negative then the resulting sum (which may already be positive or negative) is negated. Procedure isEven(x) ProcedureReturn (x & 1) ! 1 EndProcedure Procedure halveValue(x) ProcedureReturn x / 2 EndProcedure Procedure doubleValue(x) ProcedureReturn x << 1 EndProcedure Procedure EthiopianMultiply(x, y) Protected sum, sign = x Print("Ethiopian multiplication of " + Str(x) + " and " + Str(y) + " ...") Repeat If Not isEven(x) sum + y EndIf x = halveValue(x) y = doubleValue(y) Until x = 0 If sign < 0 : sum * -1: EndIf PrintN(" equals " + Str(sum)) ProcedureReturn sum EndProcedure If OpenConsole() EthiopianMultiply(17,34) EthiopianMultiply(-17,34) EthiopianMultiply(-17,-34) Print(#CRLF$ + #CRLF$+ "Press ENTER to exit") Input() CloseConsole() EndIf Output:  Ethiopian multiplication of 17 and 34 ... equals 578 Ethiopian multiplication of -17 and 34 ... equals -578 Ethiopian multiplication of -17 and -34 ... equals 578 ### QB64 PRINT multiply(17, 34) SUB twice (n AS LONG) n = n * 2 END SUB SUB halve (n AS LONG) n = n / 2 END SUB FUNCTION odd%% (n AS LONG) odd%% = (n AND 1) * -1 END FUNCTION FUNCTION multiply& (a AS LONG, b AS LONG) DIM AS LONG result, multiplicand, multiplier multiplicand = a multiplier = b WHILE multiplicand <> 0 IF odd(multiplicand) THEN result = result + multiplier halve multiplicand twice multiplier WEND multiply& = result END FUNCTION  Output: 578 ### Sinclair ZX81 BASIC Requires at least 2k of RAM. The specification is emphatic about wanting named functions: in a language where user-defined functions do not exist, the best we can do is to use subroutines and assign their line numbers to variables. This allows us to GOSUB HALVE instead of having to GOSUB 320. (It would however be more idiomatic to avoid using subroutines at all, for simple operations like these, and to refer to them by line number if they were used.)  10 LET HALVE=320 20 LET DOUBLE=340 30 LET EVEN=360 40 DIM L(20) 50 DIM R(20) 60 INPUT L(1) 70 INPUT R(1) 80 LET I=1 90 PRINT L(1),R(1) 100 IF L(I)=1 THEN GOTO 200 110 LET I=I+1 120 IF I>20 THEN STOP 130 LET X=L(I-1) 140 GOSUB HALVE 150 LET L(I)=Y 160 LET X=R(I-1) 170 GOSUB DOUBLE 180 LET R(I)=Y 190 GOTO 90 200 FOR K=1 TO I 210 LET X=L(K) 220 GOSUB EVEN 230 IF NOT Y THEN GOTO 260 240 LET R(K)=0 250 PRINT AT K-1,16;" " 260 NEXT K 270 LET A=0 280 FOR K=1 TO I 290 LET A=A+R(K) 300 NEXT K 310 GOTO 380 320 LET Y=INT (X/2) 330 RETURN 340 LET Y=X*2 350 RETURN 360 LET Y=X/2=INT (X/2) 370 RETURN 380 PRINT AT I+1,16;A  Input: 17 34 Output: 17 34 8 4 2 1 544 578 ### Tiny BASIC  REM Ethiopian multiplication LET X=17 LET Y=34 LET T=0 10 IF X<1 THEN GOTO 40 LET A=X GOSUB 400 IF E=0 THEN GOTO 20 LET T=T+Y PRINT X,", ",Y, " (kept)" GOTO 30 20 PRINT X,", ",Y 30 GOSUB 300 LET X=A LET A=Y GOSUB 200 LET Y=A GOTO 10 40 PRINT "------------" PRINT "= ",T," (sum of kept second vals)" END REM Subroutines are required, though REM they complicate the code REM -- Double -- REM A - param. 200 LET A=2*A RETURN REM -- Halve -- REM A - param. 300 LET A=A/2 RETURN REM -- Is even -- REM A - param.; E - result (0 - false) 400 LET E=A-(A/2)*2 RETURN Output: 17, 34 (kept) 8, 68 4, 136 2, 272 1, 544 (kept) ------------ = 578 (sum of kept second vals) ### True BASIC A translation of BBC BASIC. True BASIC does not have Boolean operations built-in. !RosettaCode: Ethiopian Multiplication ! True BASIC v6.007 PROGRAM EthiopianMultiplication DECLARE DEF FNdouble DECLARE DEF FNhalve DECLARE DEF FNeven LET x = 17 LET y = 34 DO IF FNeven(x) = 0 THEN LET p = p + y PRINT x,y ELSE PRINT x," ---" END IF LET x = FNhalve(x) LET y = FNdouble(y) LOOP UNTIL x = 0 PRINT " ", " ===" PRINT " ", p GET KEY done DEF FNdouble(A) = A * 2 DEF FNhalve(A) = INT(A / 2) DEF FNeven(A) = MOD(A+1,2) END  ### XBasic Translation of: Modula-2 Works with: Windows XBasic ' Ethiopian multiplication PROGRAM "ethmult" VERSION "0.0000" DECLARE FUNCTION Entry() INTERNAL FUNCTION Double(@a&&) INTERNAL FUNCTION Halve(@a&&) INTERNAL FUNCTION IsEven(a&&) FUNCTION Entry() x&& = 17 y&& = 34 tot&& = 0 DO WHILE x&& >= 1 PRINT FORMAT$("#########", x&&);
PRINT " ";
IFF IsEven(x&&) THEN
tot&& = tot&& + y&&
PRINT FORMAT$("#########", y&&); END IF PRINT Halve(@x&&) Double(@y&&) LOOP PRINT "= "; PRINT FORMAT$("#########", tot&&);
PRINT
END FUNCTION

FUNCTION Double(a&&)
a&& = 2 * a&&
END FUNCTION

FUNCTION Halve(a&&)
a&& = a&& / 2
END FUNCTION

FUNCTION IsEven(a&&)
RETURN a&& MOD 2 = 0
END FUNCTION
END PROGRAM
Output:
       17        34
8
4
2
1       544
=               578

### Yabasic

outP = 0
x = 17
y = 34

do
print x, chr$(09); if not (isEven(x)) then outP = outP + y print y else print fi if x < 2 break x = half(x) y = doub(y) loop print "=", chr$(09), outP
end

sub doub (a)
return a * 2
end sub

sub half (a)
return int(a / 2)
end sub

sub isEven (a)
return mod(a, 2) - 1
end sub


## Batch File

@echo off
:: Pick 2 random, non-zero, 2-digit numbers to send to :_main
set /a param1=%random% %% 98 + 1
set /a param2=%random% %% 98 + 1
call:_main %param1% %param2%
pause>nul
exit /b

:: This is the main function that outputs the answer in the form of "%1 * %2 = %answer%"
:_main
setlocal enabledelayedexpansion
set l0=%1
set r0=%2
set leftcount=1
set lefttempcount=0
set rightcount=1
set righttempcount=0

:: Creates an array ("l[]") with the :_halve function. %l0% is the initial left number parsed
:: This section will loop until the most recent member of "l[]" is equal to 0
:left
set /a lefttempcount=%leftcount%-1
if !l%lefttempcount%!==1 goto right
call:_halve !l%lefttempcount%!
set l%leftcount%=%errorlevel%
set /a leftcount+=1
goto left

:: Creates an array ("r[]") with the :_double function, %r0% is the initial right number parsed
:: This section will loop until it has the same amount of entries as "l[]"
:right
set /a righttempcount=%rightcount%-1
if %rightcount%==%leftcount% goto both
call:_double !r%righttempcount%!
set r%rightcount%=%errorlevel%
set /a rightcount+=1
goto right

:both
:: Creates an boolean array ("e[]") corresponding with whether or not the respective "l[]" entry is even
for /l %%i in (0,1,%lefttempcount%) do (
call:_even !l%%i!
set e%%i=!errorlevel!
)

:: Adds up all entries of "r[]" based on the value of "e[]", respectively
for /l %%i in (0,1,%lefttempcount%) do (
if !e%%i!==1 (
:: Everything from this-----------------------------
set iseven%%i=KEEP
) else (
set iseven%%i=STRIKE
)
echo L: !l%%i! R: !r%%i! - !iseven%%i!
:: To this, is for cosmetics and is optional--------

)
echo %l0% * %r0% = %answer%
exit /b

:: These are the three functions being used. The output of these functions are expressed in the errorlevel that they return
:_halve
setlocal
set /a temp=%1/2
exit /b %temp%

:_double
setlocal
set /a temp=%1*2
exit /b %temp%

:_even
setlocal
set int=%1
set /a modint=%int% %% 2
exit /b %modint%
Output:
L: 17 R: 34 - KEEP
L: 8 R: 68 - STRIKE
L: 4 R: 136 - STRIKE
L: 2 R: 272 - STRIKE
L: 1 R: 544 - KEEP
17 * 34 = 578


## BCPL

get "libhdr"

let halve(i)  = i>>1
and double(i) = i<<1
and even(i)   = (i&1) = 0

let emul(x, y)      = emulr(x, y, 0)
and emulr(x, y, ac) =
x=0 -> ac,
emulr(halve(x), double(y), even(x) -> ac, ac + y)

let start() be writef("%N*N", emul(17, 34))
Output:
578

## Bracmat

( (halve=.div$(!arg.2)) & (double=.2*!arg) & (isEven=.mod$(!arg.2):0)
& ( mul
=   a b as bs newbs result
.   !arg:(?as.?bs)
&   whl
' ( !as:? (%@:~1:?a)
& !as halve$!a:?as & !bs:? %@?b & !bs double$!b:?bs
)
& :?newbs
&   whl
' ( !as:%@?a ?as
& !bs:%@?b ?bs
& (isEven$!a|!newbs !b:?newbs) ) & 0:?result & whl ' (!newbs:%@?b ?newbs&!b+!result:?result) & !result ) & out$(mul$(17.34)) ); Output 578 ## BQN Double ← 2⊸× Halve ← ⌊÷⟜2 Odd ← 2⊸| EMul ← { times ← ↕⌈2⋆⁼𝕨 +´(Odd Halve⍟times 𝕨)/Double⍟times 𝕩 } 17 EMul 34  578  To avoid using a while loop, the iteration count is computed beforehand. ## C #include <stdio.h> #include <stdbool.h> void halve(int *x) { *x >>= 1; } void doublit(int *x) { *x <<= 1; } bool iseven(const int x) { return (x & 1) == 0; } int ethiopian(int plier, int plicand, const bool tutor) { int result=0; if (tutor) printf("ethiopian multiplication of %d by %d\n", plier, plicand); while(plier >= 1) { if ( iseven(plier) ) { if (tutor) printf("%4d %6d struck\n", plier, plicand); } else { if (tutor) printf("%4d %6d kept\n", plier, plicand); result += plicand; } halve(&plier); doublit(&plicand); } return result; } int main() { printf("%d\n", ethiopian(17, 34, true)); return 0; }  ## C# Works with: C# version 3+ Library: System.Linq using System; using System.Linq; namespace RosettaCode.Tasks { public static class EthiopianMultiplication_Task { public static void Test ( ) { Console.WriteLine ( "Ethiopian Multiplication" ); int A = 17, B = 34; Console.WriteLine ( "Recursion: {0}*{1}={2}", A, B, EM_Recursion ( A, B ) ); Console.WriteLine ( "Linq: {0}*{1}={2}", A, B, EM_Linq ( A, B ) ); Console.WriteLine ( "Loop: {0}*{1}={2}", A, B, EM_Loop ( A, B ) ); Console.WriteLine ( ); } public static int Halve ( this int p_Number ) { return p_Number >> 1; } public static int Double ( this int p_Number ) { return p_Number << 1; } public static bool IsEven ( this int p_Number ) { return ( p_Number % 2 ) == 0; } public static int EM_Recursion ( int p_NumberA, int p_NumberB ) { // Anchor Point, Recurse to find the next row Sum it with the second number according to the rules return p_NumberA == 1 ? p_NumberB : EM_Recursion ( p_NumberA.Halve ( ), p_NumberB.Double ( ) ) + ( p_NumberA.IsEven ( ) ? 0 : p_NumberB ); } public static int EM_Linq ( int p_NumberA, int p_NumberB ) { // Creating a range from 1 to x where x the number of times p_NumberA can be halved. // This will be 2^x where 2^x <= p_NumberA. Basically, ln(p_NumberA)/ln(2). return Enumerable.Range ( 1, Convert.ToInt32 ( Math.Log ( p_NumberA, Math.E ) / Math.Log ( 2, Math.E ) ) + 1 ) // For every item (Y) in that range, create a new list, comprising the pair (p_NumberA,p_NumberB) Y times. .Select ( ( item ) => Enumerable.Repeat ( new { Col1 = p_NumberA, Col2 = p_NumberB }, item ) // The aggregate method iterates over every value in the target list, passing the accumulated value and the current item's value. .Aggregate ( ( agg_pair, orig_pair ) => new { Col1 = agg_pair.Col1.Halve ( ), Col2 = agg_pair.Col2.Double ( ) } ) ) // Remove all even items .Where ( pair => !pair.Col1.IsEven ( ) ) // And sum! .Sum ( pair => pair.Col2 ); } public static int EM_Loop ( int p_NumberA, int p_NumberB ) { int RetVal = 0; while ( p_NumberA >= 1 ) { RetVal += p_NumberA.IsEven ( ) ? 0 : p_NumberB; p_NumberA = p_NumberA.Halve ( ); p_NumberB = p_NumberB.Double ( ); } return RetVal; } } }  ## C++ Using C++ templates, these kind of tasks can be implemented as meta-programs. The program runs at compile time, and the result is statically saved into regularly compiled code. Here is such an implementation without tutor, since there is no mechanism in C++ to output messages during program compilation. template<int N> struct Half { enum { Result = N >> 1 }; }; template<int N> struct Double { enum { Result = N << 1 }; }; template<int N> struct IsEven { static const bool Result = (N & 1) == 0; }; template<int Multiplier, int Multiplicand> struct EthiopianMultiplication { template<bool Cond, int Plier, int RunningTotal> struct AddIfNot { enum { Result = Plier + RunningTotal }; }; template<int Plier, int RunningTotal> struct AddIfNot <true, Plier, RunningTotal> { enum { Result = RunningTotal }; }; template<int Plier, int Plicand, int RunningTotal> struct Loop { enum { Result = Loop<Half<Plier>::Result, Double<Plicand>::Result, AddIfNot<IsEven<Plier>::Result, Plicand, RunningTotal >::Result >::Result }; }; template<int Plicand, int RunningTotal> struct Loop <0, Plicand, RunningTotal> { enum { Result = RunningTotal }; }; enum { Result = Loop<Multiplier, Multiplicand, 0>::Result }; }; #include <iostream> int main(int, char **) { std::cout << EthiopianMultiplication<17, 54>::Result << std::endl; return 0; }  ## Clojure (defn halve [n] (bit-shift-right n 1)) (defn twice [n] ; 'double' is taken (bit-shift-left n 1)) (defn even [n] ; 'even?' is the standard fn (zero? (bit-and n 1))) (defn emult [x y] (reduce + (map second (filter #(not (even (first %))) ; a.k.a. 'odd?' (take-while #(pos? (first %)) (map vector (iterate halve x) (iterate twice y))))))) (defn emult2 [x y] (loop [a x, b y, r 0] (if (= a 1) (+ r b) (if (even a) (recur (halve a) (twice b) r) (recur (halve a) (twice b) (+ r b))))))  ## CLU halve = proc (n: int) returns (int) return(n/2) end halve double = proc (n: int) returns (int) return(n*2) end double even = proc (n: int) returns (bool) return(n//2 = 0) end even e_mul = proc (a, b: int) returns (int) total: int := 0 while (a > 0) do if ~even(a) then total := total + b end a := halve(a) b := double(b) end return(total) end e_mul start_up = proc () po: stream := stream$primary_output()
stream$putl(po, int$unparse(e_mul(17, 34)))
end start_up
Output:
578

## COBOL

Translation of: Common Lisp
Works with: COBOL version 2002
Works with: OpenCOBOL version 1.1

In COBOL, double is a reserved word, so the doubling functions is named twice, instead.

       *>* Ethiopian multiplication

IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiplication.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01  l                  PICTURE 9(10) VALUE 17.
01  r                  PICTURE 9(10) VALUE 34.
01  ethiopian-multiply PICTURE 9(20).
01  product            PICTURE 9(20).
PROCEDURE DIVISION.
CALL "ethiopian-multiply" USING
BY CONTENT l, BY CONTENT r,
BY REFERENCE ethiopian-multiply
END-CALL
DISPLAY ethiopian-multiply END-DISPLAY
MULTIPLY l BY r GIVING product END-MULTIPLY
DISPLAY product END-DISPLAY
STOP RUN.
END PROGRAM ethiopian-multiplication.

IDENTIFICATION DIVISION.
PROGRAM-ID. ethiopian-multiply.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01  evenp   PICTURE 9.
88 even   VALUE 1.
88 odd    VALUE 0.
01  l       PICTURE 9(10).
01  r       PICTURE 9(10).
01  product PICTURE 9(20) VALUE ZERO.
PROCEDURE DIVISION using l, r, product.
MOVE ZEROES TO product
PERFORM UNTIL l EQUAL ZERO
CALL "evenp" USING
BY CONTENT l,
BY REFERENCE evenp
END-CALL
IF odd
ADD r TO product GIVING product END-ADD
END-IF
CALL "halve" USING
BY CONTENT l,
BY REFERENCE l
END-CALL
CALL "twice" USING
BY CONTENT r,
BY REFERENCE r
END-CALL
END-PERFORM
GOBACK.
END PROGRAM ethiopian-multiply.

IDENTIFICATION DIVISION.
PROGRAM-ID. halve.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01  n   PICTURE 9(10).
01  m   PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING m END-DIVIDE
GOBACK.
END PROGRAM halve.

IDENTIFICATION DIVISION.
PROGRAM-ID. twice.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01  n   PICTURE 9(10).
01  m   PICTURE 9(10).
PROCEDURE DIVISION USING n, m.
MULTIPLY n by 2 GIVING m END-MULTIPLY
GOBACK.
END PROGRAM twice.

IDENTIFICATION DIVISION.
PROGRAM-ID. evenp.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01  q   PICTURE 9(10).
01  n   PICTURE 9(10).
01  m   PICTURE 9(1).
88 even   VALUE 1.
88 odd    VALUE 0.
PROCEDURE DIVISION USING n, m.
DIVIDE n BY 2 GIVING q REMAINDER m END-DIVIDE
SUBTRACT m FROM 1 GIVING m END-SUBTRACT
GOBACK.
END PROGRAM evenp.


## CoffeeScript

halve = (n) -> Math.floor n / 2
double = (n) -> n * 2
is_even = (n) -> n % 2 == 0

multiply = (a, b) ->
prod = 0
while a > 0
prod += b if !is_even a
a = halve a
b = double b
prod

# tests
do ->
for i in [0..100]
for j in [0..100]
throw Error("broken for #{i} * #{j}") if multiply(i,j) != i * j


### CoffeeScript "One-liner"

ethiopian = (a, b, r=0) -> if a <= 0 then r else ethiopian a // 2, b * 2, if a % 2 then r + b else r

## ColdFusion

Version with as a function of functions:

<cffunction name="double">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number * 2>
</cffunction>

<cffunction name="halve">
<cfargument name="number" type="numeric" required="true">
<cfset answer = int(number / 2)>
</cffunction>

<cffunction name="even">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number mod 2>
</cffunction>

<cffunction name="ethiopian">
<cfargument name="Number_A" type="numeric" required="true">
<cfargument name="Number_B" type="numeric" required="true">
<cfset Result = 0>

<cfloop condition = "Number_A GTE 1">
<cfif even(Number_A) EQ 1>
<cfset Result = Result + Number_B>
</cfif>
<cfset Number_A = halve(Number_A)>
<cfset Number_B = double(Number_B)>
</cfloop>
<cfreturn Result>
</cffunction>

<cfoutput>#ethiopian(17,34)#</cfoutput>

Version with display pizza:
<cfset Number_A = 17>
<cfset Number_B = 34>
<cfset Result = 0>

<cffunction name="double">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number * 2>
</cffunction>

<cffunction name="halve">
<cfargument name="number" type="numeric" required="true">
<cfset answer = int(number / 2)>
</cffunction>

<cffunction name="even">
<cfargument name="number" type="numeric" required="true">
<cfset answer = number mod 2>
</cffunction>

<cfoutput>

Ethiopian multiplication of #Number_A# and #Number_B#...
<br>

<table width="512" border="0" cellspacing="20" cellpadding="0">

<cfloop condition = "Number_A GTE 1">

<cfif even(Number_A) EQ 1>
<cfset Result = Result + Number_B>
<cfset Action = "Keep">
<cfelse>
<cfset Action = "Strike">
</cfif>

<tr>
<td align="right">#Number_A#</td>
<td align="right">#Number_B#</td>
<td align="center">#Action#</td>
</tr>

<cfset Number_A = halve(Number_A)>
<cfset Number_B = double(Number_B)>

</cfloop>

</table>

...equals #Result#

</cfoutput>

Sample output:
Ethiopian multiplication of 17 and 34...
17 	34 	Keep
8 	68 	Strike
4 	136 	Strike
2 	272 	Strike
1 	544 	Keep
...equals 578


## Common Lisp

Common Lisp already has evenp, but all three of halve, double, and even-p are locally defined within ethiopian-multiply. (Note that the termination condition is (zerop l) because we terminate 'after' the iteration wherein the left column contains 1, and (halve 1) is 0.)
(defun ethiopian-multiply (l r)
(flet ((halve (n) (floor n 2))
(double (n) (* n 2))
(even-p (n) (zerop (mod n 2))))
(do ((product 0 (if (even-p l) product (+ product r)))
(l l (halve l))
(r r (double r)))
((zerop l) product))))


## Craft Basic

let x = 17
let y = 34
let s = 0

do

if x < 1 then

break

endif

if s = 1 then

print x

endif

if s = 0 then

let s = 1

endif

let a = x
let e = a % 2
let e = 1 - e

if e = 0 then

let t = t + y
print x, " ", y

endif

let a = x
let a = int(a / 2)
let x = a
let a = y
let a = 2 * a
let y = a

loop x >= 1

print "="
print t

Output:
17 34
8
4
2
1
1 544
=

578

## D

int ethiopian(int n1, int n2) pure nothrow @nogc
in {
assert(n1 >= 0, "Multiplier can't be negative");
} body {
static enum doubleNum = (in int n) pure nothrow @nogc => n * 2;
static enum halveNum = (in int n) pure nothrow @nogc => n / 2;
static enum isEven = (in int n) pure nothrow @nogc => !(n & 1);

int result;
while (n1 >= 1) {
if (!isEven(n1))
result += n2;
n1 = halveNum(n1);
n2 = doubleNum(n2);
}

return result;
} unittest {
assert(ethiopian(77, 54) == 77 * 54);
assert(ethiopian(8, 923) == 8 * 923);
assert(ethiopian(64, -4) == 64 * -4);
}

void main() {
import std.stdio;

writeln("17 ethiopian 34 is ", ethiopian(17, 34));
}

Output:
17 ethiopian 34 is 578


## dc

0k                    [ Make sure we're doing integer division  ]sx
[ 2 / ] sH            [ Define "halve" function in register H   ]sx
[ 2 * ] sD            [ Define "double" function in register D  ]sx
[ 2 % 1 r - ] sE      [ Define "even?" function in register E   ]sx

[ Entry into the main Ethiopian multiplication function is register M ]sx
[ Keeps running value for the product in register p ]sx
[ 0 sp lLx lp ] sM

[ The body of the main loop is in register L ]sx

[
sb sa             [ First thing we do is cheat and store the parameters in
registers, which is safe because the only recursion is of
the tail variety.  This avoids tricky stack
manipulations, which dc doesn't have good support for
(unlike, say, Forth). ]sx

la lEx sr         [ r = even?(a)  ]sx
lr 0 =S           [ if r = 0 then call s]sx
la lHx d          [ a = halve(a)]sx
lb lDx            [ b = double(b)]sx
r 0 !=L           [ if a !=0 then recurse ]
] sL

[ Utility macro that just adds the current value of b to the total in p ]sx
[ lp lb + sp ]sS

[ Demo by multiplying 17 and 34 ]sx
17 34 lMx p
Output:
578


See Pascal.

## Draco

proc nonrec halve(word n) word:  n >> 1     corp
proc nonrec double(word n) word: n << 1     corp
proc nonrec even(word n) bool:   n & 1 = 0  corp

proc nonrec emul(word a, b) word:
word total;
total := 0;
while a > 0 do
if not even(a) then total := total + b fi;
a := halve(a);
b := double(b)
od;
total
corp

proc nonrec main() void: writeln(emul(17, 34)) corp
Output:
578

## E

def halve(&x)  { x //= 2 }
def double(&x) { x *= 2 }
def even(x)    { return x %% 2 <=> 0 }

def multiply(var a, var b) {
var ab := 0
while (a > 0) {
if (!even(a)) { ab += b }
halve(&a)
double(&b)
}
return ab
}

## EasyLang

func mult x y .
while x >= 1
if x mod 2 <> 0
tot += y
.
x = x div 2
y *= 2
.
.
print mult 17 34

## Eiffel

class
APPLICATION

create
make

feature {NONE}

make
do
io.put_integer (ethiopian_multiplication (17, 34))
end

ethiopian_multiplication (a, b: INTEGER): INTEGER
-- Product of 'a' and 'b'.
require
a_positive: a > 0
b_positive: b > 0
local
x, y: INTEGER
do
x := a
y := b
from
until
x <= 0
loop
if not is_even_int (x) then
Result := Result + y
end
x := halve_int (x)
y := double_int (y)
end
ensure
Result_correct: Result = a * b
end

feature {NONE}

double_int (n: INTEGER): INTEGER
--Two times 'n'.
do
Result := n * 2
end

halve_int (n: INTEGER): INTEGER
--'n' divided by two.
do
Result := n // 2
end

is_even_int (n: INTEGER): BOOLEAN
--Is 'n' an even integer?
do
Result := n \\ 2 = 0
end

end

Output:
578


## Ela

open list number

halve x = x div 2
double = (2*)

ethiopicmult a b = sum <| map snd <| filter (odd << fst) <| zip
(takeWhile (>=1) <| iterate halve a)
(iterate double b)

ethiopicmult 17 34
Output:
578


## Elixir

Translation of: Erlang
defmodule Ethiopian do
def halve(n), do: div(n, 2)

def double(n), do: n * 2

def even(n), do: rem(n, 2) == 0

def multiply(lhs, rhs) when is_integer(lhs) and lhs > 0 and is_integer(rhs) and rhs > 0 do
multiply(lhs, rhs, 0)
end

def multiply(1, rhs, acc), do: rhs + acc
def multiply(lhs, rhs, acc) do
if even(lhs), do:   multiply(halve(lhs), double(rhs), acc),
else: multiply(halve(lhs), double(rhs), acc+rhs)
end
end

IO.inspect Ethiopian.multiply(17, 34)

Output:
578


## Emacs Lisp

Emacs Lisp has cl-evenp in cl-lib.el (its Common Lisp library), but for the sake of completeness the desired effect is achieved here via mod.

(defun even-p (n)
(= (mod n 2) 0))
(defun halve (n)
(floor n 2))
(defun double (n)
(* n 2))
(defun ethiopian-multiplication (l r)
(let ((sum 0))
(while (>= l 1)
(unless (even-p l)
(setq sum (+ r sum)))
(setq l (halve l))
(setq r (double r)))
sum))


## EMal

fun halve = int by int value do return value / 2 end
fun double = int by int value do return value * 2 end
fun isEven = logic by int value do return value % 2 == 0 end
fun ethiopian = int by int multiplicand, int multiplier
int product
while multiplicand >= 1
if not isEven(multiplicand) do product += multiplier end
multiplicand = halve(multiplicand)
multiplier = double(multiplier)
end
return product
end
writeLine(ethiopian(17, 34))
Output:
578


## Erlang

-module(ethopian).
-export([multiply/2]).

halve(N) ->
N div 2.

double(N) ->
N * 2.

even(N) ->
(N rem 2) == 0.

multiply(LHS,RHS) when is_integer(Lhs) and Lhs > 0 and
is_integer(Rhs) and Rhs > 0 ->
multiply(LHS,RHS,0).

multiply(1,RHS,Acc) ->
RHS+Acc;
multiply(LHS,RHS,Acc) ->
case even(LHS) of
true ->
multiply(halve(LHS),double(RHS),Acc);
false ->
multiply(halve(LHS),double(RHS),Acc+RHS)
end.


## ERRE

PROGRAM ETHIOPIAN_MULT

FUNCTION EVEN(A)
EVEN=(A+1) MOD 2
END FUNCTION

FUNCTION HALF(A)
HALF=INT(A/2)
END FUNCTION

FUNCTION DOUBLE(A)
DOUBLE=2*A
END FUNCTION

BEGIN
X=17 Y=34 TOT=0
WHILE X>=1 DO
PRINT(X,)
IF EVEN(X)=0 THEN TOT=TOT+Y PRINT(Y) ELSE PRINT END IF
X=HALF(X) Y=DOUBLE(Y)
END WHILE
PRINT("=",TOT)
END PROGRAM
Output:
17            34
8
4
2
1             544
=             578


## Euphoria

function emHalf(integer n)
return floor(n/2)
end function

function emDouble(integer n)
return n*2
end function

function emIsEven(integer n)
return (remainder(n,2) = 0)
end function

function emMultiply(integer a, integer b)
integer sum
sum = 0
while (a) do
if (not emIsEven(a)) then sum += b end if
a = emHalf(a)
b = emDouble(b)
end while

return sum
end function

----------------------------------------------------------------
-- runtime

printf(1,"emMultiply(%d,%d) = %d\n",{17,34,emMultiply(17,34)})

printf(1,"\nPress Any Key\n",{})
while (get_key() = -1) do end while

## F#

let ethopian n m =
let halve n = n / 2
let double n = n * 2
let even n = n % 2 = 0
let rec loop n m result =
if n <= 1 then result + m
else if even n then loop (halve n) (double m) result
else loop (halve n) (double m) (result + m)
loop n m 0


## Factor

USING: arrays kernel math multiline sequences ;
IN: ethiopian-multiplication

/*
This function is built-in
: odd? ( n -- ? ) 1 bitand 1 number= ;
*/

: double ( n -- 2*n ) 2 * ;
: halve ( n -- n/2 ) 2 /i ;

: ethiopian-mult ( a b -- a*b )
[ 0 ] 2dip
[ dup 0 > ] [
[ odd? [ + ] [ drop ] if ] 2keep
[ double ] [ halve ] bi*
] while 2drop ;


## FALSE

[2/]h:
[2*]d:
[$2/2*-]o: [0[@$][$o;![@@\$@+@]?h;!@d;!@]#%\%]m:
17 34m;!.  {578}

## Forth

Halve and double are standard words, spelled 2/ and 2* respectively.

: even? ( n -- ? ) 1 and 0= ;
: e* ( x y -- x*y )
dup 0= if nip exit then
over 2* over 2/ recurse
swap even? if nip else + then ;

The author of Forth, Chuck Moore, designed a similar primitive into his MISC Forth microprocessors. The +* instruction is a multiply step: it adds S to T if A is odd, then shifts both A and T right one. The idea is that you only need to perform as many of these multiply steps as you have significant bits in the operand.(See his core instruction set for details.)

## Fortran

Works with: Fortran version 90 and later
program EthiopicMult
implicit none

print *, ethiopic(17, 34, .true.)

contains

subroutine halve(v)
integer, intent(inout) :: v
v = int(v / 2)
end subroutine halve

subroutine doublit(v)
integer, intent(inout) :: v
v = v * 2
end subroutine doublit

function iseven(x)
logical :: iseven
integer, intent(in) :: x
iseven = mod(x, 2) == 0
end function iseven

function ethiopic(multiplier, multiplicand, tutorialized) result(r)
integer :: r
integer, intent(in) :: multiplier, multiplicand
logical, intent(in), optional :: tutorialized

integer :: plier, plicand
logical :: tutor

plier = multiplier
plicand = multiplicand

if ( .not. present(tutorialized) ) then
tutor = .false.
else
tutor = tutorialized
endif

r = 0

if ( tutor ) write(*, '(A, I0, A, I0)') "ethiopian multiplication of ", plier, " by ", plicand

do while(plier >= 1)
if ( iseven(plier) ) then
if (tutor) write(*, '(I4, " ", I6, A)') plier, plicand, " struck"
else
if (tutor) write(*, '(I4, " ", I6, A)') plier, plicand, " kept"
r = r + plicand
endif
call halve(plier)
call doublit(plicand)
end do

end function ethiopic

end program EthiopicMult


## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

Test case

Because the required functions are either simple or intrinsic, the solution can be much simpler:

## FutureBasic

local fn Doubled( n as long ) : end fn = n * 2
local fn Halved(  n as long ) : end fn = int( n / 2 )
local fn IsEven(  n as long ) : end fn = ( n mod 2 ) - 1

local fn EthiopianMultiply( x as long, y as long )
long sum = 0, sign = x
printf @"Ethiopian multiplication of %3ld x %3ld = \b", x, y
do
if not ( fn IsEven( x ) ) then sum += y
x = fn Halved( x ) : y = fn Doubled( y )
until ( x == 0 )
if sign < 0 then sum *= - 1
printf @"%4ld", sum
end fn

fn EthiopianMultiply(  17,  34 )
fn EthiopianMultiply( -17,  34 )
fn EthiopianMultiply( -17, -34 )

HandleEvents
Output:
Ethiopian multiplication of  17 x  34 =  578
Ethiopian multiplication of -17 x  34 = -578
Ethiopian multiplication of -17 x -34 =  578


## Go

package main

import "fmt"

func halve(i int) int { return i/2 }

func double(i int) int { return i*2 }

func isEven(i int) bool { return i%2 == 0 }

func ethMulti(i, j int) (r int) {
for ; i > 0; i, j = halve(i), double(j) {
if !isEven(i) {
r += j
}
}
return
}

func main() {
fmt.Printf("17 ethiopian 34 = %d\n", ethMulti(17, 34))
}


### Using integer (+)

import Prelude hiding (odd)

halve :: Int -> Int
halve = (div 2)

double :: Int -> Int
double = join (+)

odd :: Int -> Bool
odd = (== 1) . (mod 2)

ethiopicmult :: Int -> Int -> Int
ethiopicmult a b =
sum $map snd$
filter (odd . fst) $zip (takeWhile (>= 1)$ iterate halve a) (iterate double b)

main :: IO ()
main = print $ethiopicmult 17 34 == 17 * 34  Output: *Main> ethiopicmult 17 34 578 ### Fold after unfold Logging the stages of the unfoldr and foldr applications: import Data.List (inits, intercalate, unfoldr) import Data.Tuple (swap) import Debug.Trace (trace) ----------------- ETHIOPIAN MULTIPLICATION --------------- ethMult :: Int -> Int -> Int ethMult n m = ( trace =<< (<> "\n") . ((showDoubles pairs <> " = ") <>) . show ) (foldr addedWhereOdd 0 pairs) where pairs = zip (unfoldr halved n) (iterate doubled m) doubled x = x + x halved h | 0 < h = Just$
trace
(showHalf h)
(swap $quotRem h 2) | otherwise = Nothing addedWhereOdd (d, x) a | 0 < d = (+) a x | otherwise = a ---------------------- TRACE DISPLAY --------------------- showHalf :: Int -> String showHalf x = "halve: " <> rjust 6 ' ' (show (quotRem x 2)) showDoubles :: [(Int, Int)] -> String showDoubles xs = "double:\n" <> unlines (go <$> xs)
<> intercalate " + " (xs >>= f)
where
go x
| 0 < fst x = "-> " <> rjust 3 ' ' (show $snd x) | otherwise = rjust 6 ' '$ show $snd x f (r, q) | 0 < r = [show q] | otherwise = [] rjust :: Int -> Char -> String -> String rjust n c s = drop (length s) (replicate n c <> s) --------------------------- TEST ------------------------- main :: IO () main = do print$ ethMult 17 34
print $ethMult 34 17  Output: halve: (8,1) halve: (4,0) halve: (2,0) halve: (1,0) halve: (0,1) double: -> 34 68 136 272 -> 544 34 + 544 = 578 halve: (17,0) halve: (8,1) halve: (4,0) halve: (2,0) halve: (1,0) halve: (0,1) double: 17 -> 34 68 136 272 -> 544 34 + 544 = 578 578 578 ### Using monoid mappend Alternatively, we can express Ethiopian multiplication in terms of mappend and mempty, in place of (+) and 0. This additional generality means that our ethMult function can now replicate a string n times as readily as it multiplies an integer n times, or raises an integer to the nth power. import Control.Monad (join) import Data.List (unfoldr) import Data.Monoid (getProduct, getSum) import Data.Tuple (swap) ----------------- ETHIOPIAN MULTIPLICATION --------------- ethMult :: (Monoid m) => Int -> m -> m ethMult n m = foldr addedWhereOdd mempty$
zip (unfoldr half n) $iterate (join (<>)) m half :: Integral b => b -> Maybe (b, b) half n | 0 /= n = Just . swap$ quotRem n 2
| otherwise = Nothing

addedWhereOdd :: (Eq a, Num a, Semigroup p) => (a, p) -> p -> p
addedWhereOdd (d, x) a
| 0 /= d = a <> x
| otherwise = a

--------------------------- TEST -------------------------
main :: IO ()
main = do
mapM_ print $[ getSum$ ethMult 17 34, -- 34 * 17
getProduct $ethMult 3 34 -- 34 ^ 3 ] -- [3 ^ 17, 4 ^ 17] <> (getProduct <$> ([ethMult 17] <*> [3, 4]))
print $ethMult 17 "34" print$ ethMult 17 [3, 4]

Output:
578
39304
129140163
17179869184
"3434343434343434343434343434343434"
[3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4,3,4]

## HicEst

   WRITE(Messagebox) ethiopian( 17, 34 )
END ! of "main"

FUNCTION ethiopian(x, y)
ethiopian = 0
left = x
right = y
DO i = x, 1, -1
IF( isEven(left) == 0 ) ethiopian = ethiopian + right
IF( left == 1 ) RETURN
left = halve(left)
right = double(right)
ENDDO
END

FUNCTION halve( x )
halve = INT( x/2 )
END

FUNCTION double( x )
double = 2 * x
END

FUNCTION isEven( x )
isEven = MOD(x, 2) == 0
END

## Icon and Unicon

procedure main(arglist)
while ethiopian(integer(get(arglist)),integer(get(arglist)))  # multiply successive pairs of command line arguments
end

procedure ethiopian(i,j)                                      # recursive Ethiopian multiplication
return ( if not even(i) then j                                # this exploits that icon control expressions return values
else 0 ) +
( if i ~= 0 then ethiopian(halve(i),double(j))
else 0 )
end

procedure double(i)
return i * 2
end

procedure halve(i)
return i / 2
end

procedure even(i)
return ( i % 2 = 0, i )
end

While not it seems a task requirement, most implementations have a tutorial version. This seemed easiest in an iterative version.
procedure ethiopian(i,j)  # iterative tutor
local p,w
w := *j+3
write("Ethiopian Multiplication of ",i," * ",j)

p := 0
until i = 0 do {
writes(right(i,w),right(j,w))
if not even(i) then {
p +:= j
}
i := halve(i)
j := double(j)
}
write(right("=",w),right(p,w))
return p
end


## J

Solution:
double =:  2&*
halve  =:  %&2           NB.  or the primitive  -:
odd    =:  2&|

ethiop =:  +/@(odd@] # (double~ <@#)) (1>.<.@halve)^:a:


Example:

  17 ethiop 34
578


Note that double will repeatedly double its right argument if given a repetition count for its left argument:

  (<5) double 17
17 34 68 136 272

Note: this implementation assumes that the number on the right is a positive integer. In contexts where it can be negative, its absolute value should be used and you should multiply the result of ethiop by its sign.
ethio=: *@] * (ethiop |)

Alternatively, if multiplying by negative 1 is prohibited, you can use a conditional function which optionally negates its argument.
ethio=: *@] -@]^:(0 > [) (ethiop |)

Examples:
   7 ethio 11
77
7 ethio _11
_77
_7 ethio 11
_77
_7 ethio _11
77


## Java

Works with: Java version 1.5+
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
public class Mult{
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int first = sc.nextInt();
int second = sc.nextInt();

if(first < 0){
first = -first;
second = -second;
}

Map<Integer, Integer> columns = new HashMap<Integer, Integer>();
columns.put(first, second);
int sum = isEven(first)? 0 : second;
do{
first = halveInt(first);
second = doubleInt(second);
columns.put(first, second);
if(!isEven(first)){
sum += second;
}
}while(first > 1);

System.out.println(sum);
}

public static int doubleInt(int doubleMe){
return doubleMe << 1; //shift left
}

public static int halveInt(int halveMe){
return halveMe >>> 1; //shift right
}

public static boolean isEven(int num){
return (num & 1) == 0;
}
}
An optimised variant using the three helper functions from the other example.
/**
* This method will use ethiopian styled multiplication.
* @param a Any non-negative integer.
* @param b Any integer.
* @result a multiplied by b
*/
public static int ethiopianMultiply(int a, int b) {
if(a==0 || b==0) {
return 0;
}
int result = 0;
while(a>=1) {
if(!isEven(a)) {
result+=b;
}
b = doubleInt(b);
a = halveInt(a);
}
return result;
}

/**
* This method is an improved version that will use
* ethiopian styled multiplication, and also
* supports negative parameters.
* @param a Any integer.
* @param b Any integer.
* @result a multiplied by b
*/
public static int ethiopianMultiplyWithImprovement(int a, int b) {
if(a==0 || b==0) {
return 0;
}
if(a<0) {
a=-a;
b=-b;
} else if(b>0 && a>b) {
int tmp = a;
a = b;
b = tmp;
}
int result = 0;
while(a>=1) {
if(!isEven(a)) {
result+=b;
}
b = doubleInt(b);
a = halveInt(a);
}
return result;
}

## JavaScript

var eth = {

halve : function ( n ){  return Math.floor(n/2);  },
double: function ( n ){  return 2*n;              },
isEven: function ( n ){  return n%2 === 0);       },

mult: function ( a , b ){
var sum = 0, a = [a], b = [b];

while ( a[0] !== 1 ){
a.unshift( eth.halve( a[0] ) );
b.unshift( eth.double( b[0] ) );
}

for( var i = a.length - 1; i > 0 ; i -= 1 ){

if( !eth.isEven( a[i] ) ){
sum += b[i];
}
}
return sum + b[0];
}
}
// eth.mult(17,34) returns 578


Or, avoiding the use of a multiplication operator in the version above, we can alternatively:

1. Halve an integer, in this sense, with a right-shift (n >>= 1)
2. Double an integer by addition to self (m += m)
3. Test if an integer is odd by bitwise and (n & 1)

function ethMult(m, n) {
var o = !isNaN(m) ? 0 : ''; // same technique works with strings
if (n < 1) return o;
while (n > 1) {
if (n & 1) o += m;  // 3. integer odd/even? (bit-wise and 1)
n >>= 1;            // 1. integer halved (by right-shift)
m += m;             // 2. integer doubled (addition to self)
}
return o + m;
}

ethMult(17, 34)

Output:
578

Note that the same function will also multiply strings with some efficiency, particularly where n is larger. See Repeat_a_string

ethMult('Ethiopian', 34)

Output:
"EthiopianEthiopianEthiopianEthiopianEthiopianEthiopian
EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian
EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian
EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian
EthiopianEthiopianEthiopianEthiopianEthiopianEthiopianEthiopian"

## jq

The following implementation is intended for jq 1.4 and later.

If your jq has while/2, then the implementation of the inner function, pairs, can be simplified to:
def pairs: while( .[0] > 0; [ (.[0] | halve), (.[1] | double) ]);
def halve: (./2) | floor;

def double: 2 * .;

def isEven: . % 2 == 0;

def ethiopian_multiply(a;b):
def pairs: recurse( if .[0] > 0
then [ (.[0] | halve), (.[1] | double) ]
else empty
end );
reduce ([a,b] | pairs
| select( .[0] | isEven | not)
| .[1] ) as $i (0; . +$i) ;
Example:
ethiopian_multiply(17;34) # => 578

## Jsish

From Javascript entry.

/* Ethiopian multiplication in Jsish */
var eth = {
halve : function(n) { return Math.floor(n / 2); },
double: function(n) { return n << 1;            },
isEven: function(n) { return n % 2 === 0;       },

mult: function(a, b){
var sum = 0;
a = [a], b = [b];

while (a[0] !== 1) {
a.unshift(eth.halve(a[0]));
b.unshift(eth.double(b[0]));
}

for (var i = a.length - 1; i > 0; i -= 1) {
if(!eth.isEven(a[i])) sum += b[i];
}
return sum + b[0];
}
};

;eth.mult(17,34);

/*
=!EXPECTSTART!=
eth.mult(17,34) ==> 578
=!EXPECTEND!=
*/

Output:
prompt$jsish -u ethiopianMultiplication.jsi [PASS] ethiopianMultiplication.jsi ## Julia Works with: Julia version 0.6 Helper functions (type stable): halve(x::Integer) = x >> one(x) double(x::Integer) = Int8(2) * x even(x::Integer) = x & 1 != 1  Main function: function ethmult(a::Integer, b::Integer) r = 0 while a > 0 r += b * !even(a) a = halve(a) b = double(b) end return r end @show ethmult(17, 34)  Array version (more similar algorithm to the one from the task description): function ethmult2(a::Integer, b::Integer) A = [a] B = [b] while A[end] > 1 push!(A, halve(A[end])) push!(B, double(B[end])) end return sum(B[map(!even, A)]) end @show ethmult2(17, 34)  Output: ethmult(17, 34) = 578 ethmult2(17, 34) = 578 Benchmark test: julia> @time ethmult(17, 34) 0.000003 seconds (5 allocations: 176 bytes) 578 julia> @time ethmult2(17, 34) 0.000007 seconds (18 allocations: 944 bytes) 578  ## Kotlin // version 1.1.2 fun halve(n: Int) = n / 2 fun double(n: Int) = n * 2 fun isEven(n: Int) = n % 2 == 0 fun ethiopianMultiply(x: Int, y: Int): Int { var xx = x var yy = y var sum = 0 while (xx >= 1) { if (!isEven(xx)) sum += yy xx = halve(xx) yy = double(yy) } return sum } fun main(args: Array<String>) { println("17 x 34 =${ethiopianMultiply(17, 34)}")
println("99 x 99 = ${ethiopianMultiply(99, 99)}") }  Output: 17 x 34 = 578 99 x 99 = 9801  ### Literally follow the algorithm using generateSequence() fun Int.halve() = this shr 1 fun Int.double() = this shl 1 fun Int.isOdd() = this and 1 == 1 fun ethiopianMultiply(n: Int, m: Int): Int = generateSequence(Pair(n, m)) { p -> Pair(p.first.halve(), p.second.double()) } .takeWhile { it.first >= 1 }.filter { it.first.isOdd() }.sumOf { it.second } fun main() { ethiopianMultiply(17, 34).also { println(it) } // 578 ethiopianMultiply(99, 99).also { println(it) } // 9801 ethiopianMultiply(4, 8).also { println(it) } // 32 }  ## Lambdatalk A translation from the javascript entry. {def halve {lambda {:n} {floor {/ :n 2}}}} -> halve {def double {lambda {:n} {* 2 :n}}} -> double {def isEven {lambda {:n} {= {% :n 2} 0}}} -> isEven {def mult {def mult.r {lambda {:a :b} {if {= {A.first :a} 1} then {+ {S.map {{lambda {:a :b :i} {if {isEven {A.get :i :a}} then else {A.get :i :b}}} :a :b} {S.serie {- {A.length :a} 1} 0 -1}}} else {mult.r {A.addfirst! {halve {A.first :a}} :a} {A.addfirst! {double {A.first :b}} :b}}}}} {lambda {:a :b} {mult.r {A.new :a} {A.new :b}}}} -> mult {mult 17 34} -> 578  ## Limbo implement Ethiopian; include "sys.m"; sys: Sys; print: import sys; include "draw.m"; draw: Draw; Ethiopian : module { init : fn(ctxt : ref Draw->Context, args : list of string); }; init (ctxt: ref Draw->Context, args: list of string) { sys = load Sys Sys->PATH; print("\n%d\n", ethiopian(17, 34, 0)); print("\n%d\n", ethiopian(99, 99, 1)); } halve(n: int): int { return (n /2); } double(n: int): int { return (n * 2); } iseven(n: int): int { return ((n%2) == 0); } ethiopian(a: int, b: int, tutor: int): int { product := 0; if (tutor) print("\nmultiplying %d x %d", a, b); while (a >= 1) { if (!(iseven(a))) { if (tutor) print("\n%3d %d", a, b); product += b; } else if (tutor) print("\n%3d ----", a); a = halve(a); b = double(b); } return product; }  ## Locomotive Basic 10 DEF FNiseven(a)=(a+1) MOD 2 20 DEF FNhalf(a)=INT(a/2) 30 DEF FNdouble(a)=2*a 40 x=17:y=34:tot=0 50 WHILE x>=1 60 PRINT x, 70 IF FNiseven(x)=0 THEN tot=tot+y:PRINT y ELSE PRINT 80 x=FNhalf(x):y=FNdouble(y) 90 WEND 100 PRINT "=", tot Output:  17 34 8 4 2 1 544 = 578  ## Logo to double :x output ashift :x 1 end to halve :x output ashift :x -1 end to even? :x output equal? 0 bitand 1 :x end to eproduct :x :y if :x = 0 [output 0] ifelse even? :x ~ [output eproduct halve :x double :y] ~ [output :y + eproduct halve :x double :y] end ## LOLCODE HAI 1.3 HOW IZ I Halve YR Integer FOUND YR QUOSHUNT OF Integer AN 2 IF U SAY SO HOW IZ I Dubble YR Integer FOUND YR PRODUKT OF Integer AN 2 IF U SAY SO HOW IZ I IzEven YR Integer FOUND YR BOTH SAEM 0 AN MOD OF Integer AN 2 IF U SAY SO HOW IZ I EthiopianProdukt YR a AN YR b I HAS A Result ITZ 0 IM IN YR Loop UPPIN YR x WILE DIFFRINT a AN 0 NOT I IZ IzEven YR a MKAY O RLY? YA RLY Result R SUM OF Result AN b OIC a R I IZ Halve YR a MKAY b R I IZ Dubble YR b MKAY IM OUTTA YR Loop FOUND YR Result IF U SAY SO VISIBLE I IZ EthiopianProdukt YR 17 AN YR 34 MKAY KTHXBYE Output: 578 ## Lua function halve(a) return a/2 end function double(a) return a*2 end function isEven(a) return a%2 == 0 end function ethiopian(x, y) local result = 0 while (x >= 1) do if not isEven(x) then result = result + y end x = math.floor(halve(x)) y = double(y) end return result; end print(ethiopian(17, 34))  ## M2000 Interpreter Module EthiopianMultiplication{ Form 60, 25 Const Center=2, ColumnWith=12 Report Center,"Ethiopian Method of Multiplication" // using decimals as unsigned integers Def Decimal leftval, rightval, sum (leftval, rightval)=(random(1, 65535), random(1, 65536)) Print$( , ColumnWith), "Target:", leftval*rightval,
Hex  leftval*rightval
sum=0
if @IsEven(leftval) Else sum+=rightval
Print leftval, rightval,
Hex  leftval, rightval
while leftval>1
leftval=@halveInt(leftval)
rightval=@DoubleInt(rightval)
Print leftval, rightval,
Hex  leftval, rightval
if @IsEven(leftval) Else sum+=rightval
End while
Print "", sum
Hex  "", sum
Function HalveInt(i)
=Binary.Shift(i,-1)
End Function
Function DoubleInt(i)
=Binary.Shift(i,1)
End Function
Function IsEven(i)
=Binary.And(i, 1)=0
End Function
}
EthiopianMultiplication

## Mathematica / Wolfram Language

IntegerHalving[x_]:=Floor[x/2]
IntegerDoubling[x_]:=x*2;
OddInteger           OddQ
Ethiopian[x_, y_] :=
Total[Select[NestWhileList[{IntegerHalving[#[[1]]],IntegerDoubling[#[[2]]]}&, {x,y}, (#[[1]]>1&)], OddQ[#[[1]]]&]][[2]]

Ethiopian[17, 34]


Output:

578

## MATLAB

First we define the three subroutines needed for this task. These must be saved in their own individual ".m" files. The file names must be the same as the function name stored in that file. Also, they must be saved in the same directory as the script that performs the Ethiopian Multiplication.

In addition, with the exception of the "isEven" and "doubleInt" functions, the inputs of the functions have to be an integer data type. This means that the input to these functions must be coerced from the default IEEE754 double precision floating point data type that all numbers and variables are represented as, to integer data types. As of MATLAB 2007a, 64-bit integer arithmetic is not supported. So, at best, these will work for 32-bit integer data types.

halveInt.m:

function result = halveInt(number)

result = idivide(number,2,'floor');

end


doubleInt.m:

function result = doubleInt(number)

result = times(2,number);

end


isEven.m:

%Returns a logical 1 if the number is even, 0 otherwise.
function trueFalse = isEven(number)

trueFalse = logical( mod(number,2)==0 );

end


ethiopianMultiplication.m:

function answer = ethiopianMultiplication(multiplicand,multiplier)

%Generate columns
while multiplicand(end)>1
multiplicand(end+1,1) = halveInt( multiplicand(end) );
multiplier(end+1,1) = doubleInt( multiplier(end) );
end

%Strike out appropriate rows
multiplier( isEven(multiplicand) ) = [];

end


Sample input: (with data type coercion)

ethiopianMultiplication( int32(17),int32(34) )

ans =

578


## Maxima

/* Function to halve */
halve(n):=floor(n/2)$/* Function to double */ double(n):=2*n$

/* Predicate function to check wether an integer is even */
my_evenp(n):=if mod(n,2)=0 then true$/* Function that implements ethiopian function using the three previously defined functions */ ethiopian(n1,n2):=block(cn1:n1,cn2:n2,list_w:[], while cn1>0 do (list_w:endcons(cn1,list_w),cn1:halve(cn1)), n2_list:append([cn2],makelist(cn2:double(cn2),length(list_w)-1)), sublist_indices(list_w,lambda([x],not my_evenp(x))), makelist(n2_list[i],i,%%), apply("+",%%))$


## Metafont

Implemented without the tutor.

vardef halve(expr x) = floor(x/2) enddef;
vardef double(expr x) = x*2 enddef;
vardef iseven(expr x) = if (x mod 2) = 0: true else: false fi enddef;

primarydef a ethiopicmult b =
begingroup
save r_, plier_, plicand_;
plier_ := a; plicand_ := b;
r_ := 0;
forever: exitif plier_ < 1;
if not iseven(plier_): r_ := r_ + plicand_; fi
plier_ := halve(plier_);
plicand_ := double(plicand_);
endfor
r_
endgroup
enddef;

show( (17 ethiopicmult 34) );
end

## МК-61/52

П1	П2	<->	П0
ИП0	1	-	x#0	29
ИП1	2	*	П1
ИП0	2	/	[x]	П0
2	/	{x}	x#0	04	ИП2	ИП1	+	П2
БП	04
ИП2	С/П


## MMIX

In order to assemble and run this program you'll have to install MMIXware from [1]. This provides you with a simple assembler, a simulator, example programs and full documentation.

A	IS	17
B	IS	34

pliar	IS 	$255 % designating main registers pliand GREG acc GREG str IS pliar % reuse reg$255 for printing

LOC	Data_Segment
GREG	@
BUF	OCTA	#3030303030303030 % reserve a buffer that is big enough to hold
OCTA	#3030303030303030 % a max (signed) 64 bit integer:
OCTA	#3030300a00000000 %   2^63 - 1 = 9223372036854775807
% string is terminated with NL, 0

LOC	#1000		% locate program at address
GREG	@
halve	SR	pliar,pliar,1
GO	$127,$127,0

double	SL	pliand,pliand,1
GO	$127,$127,0

odd	DIV	$77,pliar,2 GET$78,rR
GO	$127,$127,0

% Main is the entry point of the program
Main 	SET	pliar,A		% initialize registers for calculation
SET	pliand,B
SET	acc,0
1H	GO	$127,odd BZ$78,2F		% if pliar is even skip incr. acc with pliand
2H	GO	$127,halve % halve pliar GO$127,double	% and double pliand
PBNZ	pliar,1B	% repeat from 1H while pliar > 0
// result: acc = 17 x 34
// next: print result --> stdout
// $0 is a temp register LDA str,BUF+19 % points after the end of the string 2H SUB str,str,1 % update buffer pointer DIV acc,acc,10 % do a divide and mod GET$0,rR		% get digit from special purpose reg. rR
% containing the remainder of the division
INCL	$0,'0' % convert to ascii STBU$0,str		% place digit in buffer
PBNZ	acc,2B		% next
% 'str' points to the start of the result
TRAP	0,Fputs,StdOut	% output answer to stdout
TRAP	0,Halt,0	% exit

Assembling:

~/MIX/MMIX/Progs> mmixal ethiopianmult.mms

Running:

~/MIX/MMIX/Progs> mmix ethiopianmult
578

## Modula-2

Works with: ADW Modula-2 version any (Compile with the linker option Console Application).
MODULE EthiopianMultiplication;

FROM SWholeIO IMPORT
WriteCard;
FROM STextIO IMPORT
WriteString, WriteLn;

PROCEDURE Halve(VAR A: CARDINAL);
BEGIN
A := A / 2;
END Halve;

PROCEDURE Double(VAR A: CARDINAL);
BEGIN
A := 2 * A;
END Double;

PROCEDURE IsEven(A: CARDINAL): BOOLEAN;
BEGIN
RETURN A REM 2 = 0;
END IsEven;

VAR
X, Y, Tot: CARDINAL;

BEGIN
X := 17;
Y := 34;
Tot := 0;
WHILE X >= 1 DO
WriteCard(X, 9);
WriteString(" ");
IF NOT(IsEven(X)) THEN
INC(Tot, Y);
WriteCard(Y, 9)
END;
WriteLn;
Halve(X);
Double(Y);
END;
WriteString("=         ");
WriteCard(Tot, 9);
WriteLn;
END EthiopianMultiplication.

Output:
       17        34
8
4
2
1       544
=               578


## Modula-3

MODULE Ethiopian EXPORTS Main;

IMPORT IO, Fmt;

PROCEDURE IsEven(n: INTEGER): BOOLEAN =
BEGIN
RETURN n MOD 2 = 0;
END IsEven;

PROCEDURE Double(n: INTEGER): INTEGER =
BEGIN
RETURN n * 2;
END Double;

PROCEDURE Half(n: INTEGER): INTEGER =
BEGIN
RETURN n DIV 2;
END Half;

PROCEDURE Multiply(a, b: INTEGER): INTEGER =
VAR
temp := 0;
plier := a;
plicand := b;
BEGIN
WHILE plier >= 1 DO
IF NOT IsEven(plier) THEN
temp := temp + plicand;
END;
plier := Half(plier);
plicand := Double(plicand);
END;
RETURN temp;
END Multiply;

BEGIN
IO.Put("17 times 34 = " & Fmt.Int(Multiply(17, 34)) & "\n");
END Ethiopian.

## MUMPS

HALVE(I)
;I should be an integer
QUIT I\2
DOUBLE(I)
;I should be an integer
QUIT I*2
ISEVEN(I)
;I should be an integer
QUIT '(I#2)
E2(M,N)
New W,A,E,L Set W=$Select($Length(M)>=$Length(N):$Length(M)+2,1:$L(N)+2),A=0,L=0,A(L,1)=M,A(L,2)=N Write "Multiplying two numbers:" For Write !,$Justify(A(L,1),W),?W,$Justify(A(L,2),W) Write:$$ISEVEN(A(L,1)) ?(2*W)," Struck" Set:'$$ISEVEN(A(L,1)) A=A+A(L,2) Set L=L+1,A(L,1)=$$HALVE(A(L-1,1)),A(L,2)=$$DOUBLE(A(L-1,2)) Quit:A(L,1)<1 Write ! For E=W:1:(2*W) Write ?E,"=" Write !,?W,$Justify(A,W),!
Kill W,A,E,L
Q
Output:
USER>D E2^ROSETTA(1439,7)
Multiplying two numbers:
1439     7
719    14
359    28
179    56
89   112
44   224 Struck
22   448 Struck
11   896
5  1792
2  3584 Struck
1  7168
=======
10073


## Nemerle

using System;
using System.Console;

module Ethiopian
{
Multiply(x : int, y : int) : int
{
def halve(a)  {a / 2}
def doble(a)  {a * 2}
def isEven(a) {a % 2 == 0}
def multiply(p, q)
{
match(p)
{
|p when (p < 1) => 0
|p when (isEven(p)) => 0 + multiply(halve(p), doble(q))
|_ => q + multiply(halve(p), doble(q))
}
}
multiply(x, y)
}

Main() : void
{
WriteLine("By Ethiopian multiplication, 17 * 34 = {0}", Multiply(17, 34));
}
}


## NetRexx

Translation of: REXX
/* NetRexx */
options replace format comments java crossref savelog symbols nobinary

/*REXX program multiplies 2 integers by Ethiopian/Russian peasant method*/
numeric digits 1000              /*handle extremely large integers.     */
/*handles zeroes and negative integers.*/
/*A & B  should be checked if integers.*/
parse arg a b .
say 'a=' a
say 'b=' b
say 'product=' emult(a,b)
return

method emult(x,y) private static
parse x x 1 ox
prod=0
loop while x\==0
if \iseven(x) then prod=prod+y
x=halve(x)
y=dubble(y)
end
return prod*ox.sign

method halve(x) private static
return x % 2

method dubble(x) private static
return x + x

method iseven(x) private static
return x//2 == 0

## Nim

proc halve(x: int): int = x div 2
proc double(x: int): int = x * 2
proc odd(x: int): bool = x mod 2 != 0

proc ethiopian(x, y: int): int =
var x = x
var y = y

while x >= 1:
if odd(x):
result += y
x = halve x
y = double y

echo ethiopian(17, 34)

Output:
578

## Objeck

Translation of: Java
use Collection;

class EthiopianMultiplication {
function : Main(args : String[]) ~ Nil {
"----"->PrintLine();
Mul(first, second)->PrintLine();
}

function : native : Mul(first : Int, second : Int) ~ Int {
if(first < 0){
first := -1 * first;
second := -1 * second;
};

sum := isEven(first)? 0 : second;
do {
first := halveInt(first);
second := doubleInt(second);
if(isEven(first) = false){
sum += second;
};
}
while(first > 1);

return sum;
}

function : halveInt(num : Int) ~ Bool {
return num >> 1;
}

function : doubleInt(num : Int) ~ Bool {
return num << 1;
}

function : isEven(num : Int) ~ Bool {
return (num and 1) = 0;
}
}

## Object Pascal

multiplication.pas:
unit Multiplication;
interface

function Double(Number: Integer): Integer;
function Halve(Number: Integer): Integer;
function Even(Number: Integer): Boolean;
function Ethiopian(NumberA, NumberB: Integer): Integer;

implementation
function Double(Number: Integer): Integer;
begin
result := Number * 2
end;

function Halve(Number: Integer): Integer;
begin
result := Number div 2
end;

function Even(Number: Integer): Boolean;
begin
result := Number mod 2 = 0
end;

function Ethiopian(NumberA, NumberB: Integer): Integer;
begin
result := 0;
while NumberA >= 1 do
begin
if not Even(NumberA) then
result := result + NumberB;
NumberA := Halve(NumberA);
NumberB := Double(NumberB)
end
end;
begin
end.

ethiopianmultiplication.pas:
program EthiopianMultiplication;

uses
Multiplication;

begin
WriteLn('17 * 34 = ', Ethiopian(17, 34))
end.

Output:
17 * 34 = 578


## Objective-C

Using class methods except for the generic useful function iseven.

#import <stdio.h>

BOOL iseven(int x)
{
return (x&1) == 0;
}

@interface EthiopicMult : NSObject
+ (int)mult: (int)plier by: (int)plicand;
+ (int)halve: (int)a;
+ (int)double: (int)a;
@end

@implementation EthiopicMult
+ (int)mult: (int)plier by: (int)plicand
{
int r = 0;
while(plier >= 1) {
if ( !iseven(plier) ) r += plicand;
plier = [EthiopicMult halve: plier];
plicand = [EthiopicMult double: plicand];
}
return r;
}

+ (int)halve: (int)a
{
return (a>>1);
}

+ (int)double: (int)a
{
return (a<<1);
}
@end

int main()
{
@autoreleasepool {
printf("%d\n", [EthiopicMult mult: 17 by: 34]);
}
return 0;
}


## OCaml

(* We optimize a bit by not keeping the intermediate lists, and summing
the right column on-the-fly, like in the C version.
The function takes "halve" and "double" operators and "is_even" predicate as arguments,
but also "is_zero", "zero" and "add". This allows for more general uses of the
ethiopian multiplication. *)
let ethiopian is_zero is_even halve zero double add b a =
let rec g a b r =
if is_zero a
then (r)
else g (halve a) (double b) (if not (is_even a) then (add b r) else (r))
in
g a b zero
;;

let imul =
ethiopian (( = ) 0) (fun x -> x mod 2 = 0) (fun x -> x / 2) 0 (( * ) 2) ( + );;

imul 17 34;;
(* - : int = 578 *)

(* Now, we have implemented the same algorithm as "rapid exponentiation",
merely changing operator names *)
let ipow =
ethiopian (( = ) 0) (fun x -> x mod 2 = 0) (fun x -> x / 2) 1 (fun x -> x*x) ( * )
;;

ipow 2 16;;
(* - : int = 65536 *)

(* still renaming operators, if "halving" is just subtracting one,
and "doubling", adding one, then we get an addition *)
let iadd a b =
ethiopian (( = ) 0) (fun x -> false) (pred) b (function x -> x) (fun x y -> succ y) 0 a
;;

(* - : int = 1421 *)

(* One can do much more with "ethiopian multiplication",
since the two "multiplicands" and the result may be of three different types,
as shown by the typing system of ocaml *)

ethiopian;;
- : ('a -> bool) ->          (* is_zero *)
('a -> bool) ->          (* is_even *)
('a -> 'a) ->            (* halve *)
'b ->                    (* zero *)
('c -> 'c) ->            (* double *)
('c -> 'b -> 'b) ->      (* add *)
'c ->                    (* b *)
'a ->                    (* a *)
'b                       (* result *)
= <fun>

(* Here zero is the starting value for the accumulator of the sums
of values in the right column in the original algorithm. But the "add"
me do something else, see for example the RosettaCode page on
"Exponentiation operator". *)


## Octave

function r = halve(a)
r = floor(a/2);
endfunction

function r = doublit(a)
r = a*2;
endfunction

function r = iseven(a)
r = mod(a,2) == 0;
endfunction

function r = ethiopicmult(plier, plicand, tutor=false)
r = 0;
if (tutor)
printf("ethiopic multiplication of %d and %d\n", plier, plicand);
endif
while(plier >= 1)
if ( iseven(plier) )
if (tutor)
printf("%4d %6d struck\n", plier, plicand);
endif
else
r = r + plicand;
if (tutor)
printf("%4d %6d kept\n", plier, plicand);
endif
endif
plier = halve(plier);
plicand = doublit(plicand);
endwhile
endfunction

disp(ethiopicmult(17, 34, true))


## Oforth

Based on Forth version.

isEven is already defined for Integers.

: halve   2 / ;
: double  2 * ;

: ethiopian
dup ifZero: [ nip return ]
over double over halve ethiopian
swap isEven ifTrue: [ nip ] else: [ + ] ;
Output:
17 34 ethiopian .
578


## Ol

(define (ethiopian-multiplication l r)
(let ((even? (lambda (n)
(eq? (mod n 2) 0))))

(let loop ((sum 0) (l l) (r r))
(print "sum: " sum ", l: " l ", r: " r)
(if (eq? l 0)
sum
(loop
(if (even? l) (+ sum r) sum)
(floor (/ l 2)) (* r 2))))))

(print (ethiopian-multiplication 17 34))
Output:
sum: 0, l: 17, r: 34
sum: 0, l: 8, r: 68
sum: 68, l: 4, r: 136
sum: 204, l: 2, r: 272
sum: 476, l: 1, r: 544
sum: 476, l: 0, r: 1088
476


## ooRexx

The Rexx solution shown herein applies equally to ooRexx.

## Oz

declare
fun {Halve X}   X div 2             end
fun {Double X}  X * 2               end
fun {Even X}    {Abs X mod 2} == 0  end  %% standard function: Int.isEven

fun {EthiopicMult X Y}
X >= 0 = true %% assert: X must not be negative

Rows = for
L in X; L>0;  {Halve L}  %% C-like iterator: "Init; While; Next"
R in Y; true; {Double R}
collect:Collect
do
{Collect L#R}
end

OddRows = {Filter Rows LeftIsOdd}
RightColumn = {Map OddRows SelectRight}
in
{Sum RightColumn}
end

%% Helpers
fun {LeftIsOdd L#_}   {Not {Even L}}          end
fun {SelectRight _#R} R                       end
fun {Sum Xs}          {FoldL Xs Number.'+' 0} end
in
{Show {EthiopicMult 17 34}}

## PARI/GP

halve(n)=n\2;
double(n)=2*n;
even(n)=!(n%2);
multE(a,b)={ my(d=0);
while(a,
if(!even(a),
d+=b);
a=halve(a);
b=double(b));
d
};

## Pascal

program EthiopianMultiplication;
{$IFDEF FPC} {$MODE DELPHI}
{$ENDIF} function Double(Number: Integer): Integer; begin Result := Number * 2 end; function Halve(Number: Integer): Integer; begin Result := Number div 2 end; function Even(Number: Integer): Boolean; begin Result := Number mod 2 = 0 end; function Ethiopian(NumberA, NumberB: Integer): Integer; begin Result := 0; while NumberA >= 1 do begin if not Even(NumberA) then Result := Result + NumberB; NumberA := Halve(NumberA); NumberB := Double(NumberB) end end; begin Write(Ethiopian(17, 34)) end.  ## Perl use strict; sub halve { int((shift) / 2); } sub double { (shift) * 2; } sub iseven { ((shift) & 1) == 0; } sub ethiopicmult { my ($plier, $plicand,$tutor) = @_;
print "ethiopic multiplication of $plier and$plicand\n" if $tutor; my$r = 0;
while ($plier >= 1) {$r += $plicand unless iseven($plier);
if ($tutor) { print "$plier, $plicand ", (iseven($plier) ? " struck" : " kept"), "\n";
}
$plier = halve($plier);
$plicand = double($plicand);
}
return $r; } print ethiopicmult(17,34, 1), "\n";  ## Phix Translation of: Euphoria function emHalf(integer n) return floor(n/2) end function function emDouble(integer n) return n*2 end function function emIsEven(integer n) return (remainder(n,2)=0) end function function emMultiply(integer a, integer b) integer sum = 0 while a!=0 do if not emIsEven(a) then sum += b end if a = emHalf(a) b = emDouble(b) end while return sum end function printf(1,"emMultiply(%d,%d) = %d\n",{17,34,emMultiply(17,34)})  ## PHP Not object oriented version: <?php function halve($x)
{
return floor($x/2); } function double($x)
{
return $x*2; } function iseven($x)
{
return !($x & 0x1); } function ethiopicmult($plier, $plicand,$tutor)
{
if ($tutor) echo "ethiopic multiplication of$plier and $plicand\n";$r = 0;
while($plier >= 1) { if ( !iseven($plier) ) $r +=$plicand;
if ($tutor) echo "$plier, $plicand ", (iseven($plier) ? "struck" : "kept"), "\n";
$plier = halve($plier);
$plicand = double($plicand);
}
return $r; } echo ethiopicmult(17, 34, true), "\n"; ?>  Output: ethiopic multiplication of 17 and 34 17, 34 kept 8, 68 struck 4, 136 struck 2, 272 struck 1, 544 kept 578  Object Oriented version: Works with: PHP5 <?php class ethiopian_multiply { protected$result = 0;

protected function __construct($x,$y){
while($x >= 1){$this->sum_result($x,$y);
$x =$this->half_num($x);$y = $this->double_num($y);
}
}

protected function half_num($x){ return floor($x/2);
}

protected function double_num($y){ return$y*2;
}

protected function not_even($n){ return$n%2 != 0 ? true : false;
}

protected function sum_result($x,$y){
if($this->not_even($x)){
$this->result +=$y;
}
}

protected function get_result(){
return $this->result; } static public function init($x, $y){$init = new ethiopian_multiply($x,$y);
return $init->get_result(); } } echo ethiopian_multiply::init(17, 34); ?>  ## Picat ### Iterative ethiopian(Multiplier, Multiplicand) = ethiopian(Multiplier, Multiplicand,false). ethiopian(Multiplier, Multiplicand,Tutor) = Result => if Tutor then printf("\n%d * %d:\n",Multiplier, Multiplicand) end, Result1 = 0, while (Multiplier >= 1) OldResult = Result1, if not even(Multiplier) then Result1 := Result1 + Multiplicand end, if Tutor then printf("%6d % 8s\n",Multiplier,cond(OldResult=Result1,"--",Multiplicand.to_string())) end, Multiplier := halve(Multiplier), Multiplicand := double(Multiplicand) end, if Tutor then println(" ======="), printf(" %8s\n",Result1.to_string()), nl end, Result = Result1. ### Recursion Translation of: Prolog ethiopian2(First,Second,Product) => ethiopian2(First,Second,0,Product). ethiopian2(1,Second,Sum0,Sum) => Sum = Sum0 + Second. ethiopian2(First,Second,Sum0,Sum) => Sum1 = Sum0 + Second*(First mod 2), ethiopian2(halve(First), double(Second), Sum1, Sum). halve(X) = X div 2. double(X) = 2*X. is_even(X) => X mod 2 = 0. ### Test go => println(ethiopian(17,34)), ethiopian2(17,34,Z2), println(Z2), println(ethiopian(17,34,true)), _ = random2(), _ = ethiopian(random() mod 10000,random() mod 10000,true), nl. Output: 578 578 17 * 34: 17 34 8 -- 4 -- 2 -- 1 544 ======= 578 578 5516 * 9839: 5516 -- 2758 -- 1379 39356 689 78712 344 -- 172 -- 86 -- 43 1259392 21 2518784 10 -- 5 10075136 2 -- 1 40300544 ======= 54271924 ## PicoLisp (de halve (N) (/ N 2) ) (de double (N) (* N 2) ) (de even? (N) (not (bit? 1 N)) ) (de ethiopian (X Y) (let R 0 (while (>= X 1) (or (even? X) (inc 'R Y)) (setq X (halve X) Y (double Y) ) ) R ) ) ## Pike int ethopian_multiply(int l, int r) { int halve(int n) { return n/2; }; int double(int n) { return n*2; }; int(0..1) evenp(int n) { return !(n%2); }; int product = 0; do { write("%5d %5d\n", l, r); if (!evenp(l)) product += r; l = halve(l); r = double(r); } while(l); return product; }  ## PL/I  declare (L(30), R(30)) fixed binary; declare (i, s) fixed binary; L, R = 0; put skip list ('Hello, please type two values and I will print their product:'); get list (L(1), R(1)); put edit ('The product of ', trim(L(1)), ' and ', trim(R(1)), ' is ') (a); do i = 1 by 1 while (L(i) ^= 0); L(i+1) = halve(L(i)); R(i+1) = double(R(i)); end; s = 0; do i = 1 by 1 while (L(i) > 0); if odd(L(i)) then s = s + R(i); end; put edit (trim(s)) (a); halve: procedure (k) returns (fixed binary); declare k fixed binary; return (k/2); end halve; double: procedure (k) returns (fixed binary); declare k fixed binary; return (2*k); end; odd: procedure (k) returns (bit (1)); return (iand(k, 1) ^= 0); end odd; ## PL/M Translation of: Action! Works with: 8080 PL/M Compiler ... under CP/M (or an emulator) 100H: /* ETHIOPIAN MULTIPLICATION */ /* CP/M SYSTEM CALL AND I/O ROUTINES */ BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; PR$CHAR:   PROCEDURE( C ); DECLARE C BYTE;    CALL BDOS( 2, C );  END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; PR$NL:     PROCEDURE;   CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */ DECLARE N ADDRESS; DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR ); N$STR( W ) = '$'; N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); END; CALL PR$STRING( .N$STR( W ) ); END PR$NUMBER;

/* RETURNS THE RESULT OF A * B USING ETHOPIAN MULTIPLICATION              */
ETHIOPIAN$MULTIPLICATION: PROCEDURE( A, B )ADDRESS; DECLARE ( A, B ) ADDRESS; DECLARE RES ADDRESS; CALL PR$STRING( .'ETHIOPIAN MULTIPLICATION OF $' ); CALL PR$NUMBER( A );
CALL PR$STRING( .' BY$' );
CALL PR$NUMBER( B ); CALL PR$NL;

RES = 0;
DO WHILE A >= 1;
CALL PR$NUMBER( A ); CALL PR$CHAR( ' ' );
CALL PR$NUMBER( B ); IF A MOD 2 = 0 THEN DO; CALL PR$STRING( .' STRIKE$' ); END; ELSE DO; CALL PR$STRING( .' KEEP$' ); RES = RES + B; END; CALL PR$NL;
A = SHR( A, 1 );
B = SHL( B, 1 );
END;
RETURN( RES );
END ETHIOPIAN$MULTIPLICATION; DECLARE RES ADDRESS; RES = ETHIOPIAN$MULTIPLICATION( 17, 34 );
CALL PR$STRING( .'RESULT IS$' );
CALL PR$NUMBER( RES ); EOF Output: ETHIOPIAN MULTIPLICATION OF 17 BY 34 17 34 KEEP 8 68 STRIKE 4 136 STRIKE 2 272 STRIKE 1 544 KEEP RESULT IS 578  ## PL/SQL This code was taken from the ADA example above - very minor differences. create or replace package ethiopian is function multiply ( left in integer, right in integer) return integer; end ethiopian; / create or replace package body ethiopian is function is_even(item in integer) return boolean is begin return item mod 2 = 0; end is_even; function double(item in integer) return integer is begin return item * 2; end double; function half(item in integer) return integer is begin return trunc(item / 2); end half; function multiply ( left in integer, right in integer) return Integer is temp integer := 0; plier integer := left; plicand integer := right; begin loop if not is_even(plier) then temp := temp + plicand; end if; exit when plier <= 1; plier := half(plier); plicand := double(plicand); end loop; return temp; end multiply; end ethiopian; / /* example call */ begin dbms_output.put_line(ethiopian.multiply(17, 34)); end; / ## Plain English \All required helper routines already exist in Plain English: \ \To cut a number in half: \Divide the number by 2. \ \To double a number: \Add the number to the number. \ \To decide if a number is odd: \Privatize the number. \Bitwise and the number with 1. \If the number is 0, say no. \Say yes. To run: Start up. Put 17 into a number. Multiply the number by 34 (Ethiopian). Convert the number to a string. Write the string to the console. Wait for the escape key. Shut down. To multiply a number by another number (Ethiopian): Put 0 into a sum number. Loop. If the number is 0, break. If the number is odd, add the other number to the sum. Cut the number in half. Double the other number. Repeat. Put the sum into the number. Output: 578  ## Powerbuilder public function boolean wf_iseven (long al_arg);return mod(al_arg, 2 ) = 0 end function public function long wf_halve (long al_arg);RETURN int(al_arg / 2) end function public function long wf_double (long al_arg);RETURN al_arg * 2 end function public function long wf_ethiopianmultiplication (long al_multiplicand, long al_multiplier);// calculate result long ll_product DO WHILE al_multiplicand >= 1 IF wf_iseven(al_multiplicand) THEN // do nothing ELSE ll_product += al_multiplier END IF al_multiplicand = wf_halve(al_multiplicand) al_multiplier = wf_double(al_multiplier) LOOP return ll_product end function // example call long ll_answer ll_answer = wf_ethiopianmultiplication(17,34) ## PowerShell ### Traditional function isEven { param ([int]$value)
return [bool]($value % 2 -eq 0) } function doubleValue { param ([int]$value)
return [int]($value * 2) } function halveValue { param ([int]$value)
return [int]($value / 2) } function multiplyValues { param ( [int]$plier,
[int]$plicand, [int]$temp = 0
)

while ($plier -ge 1) { if (!(isEven$plier)) {
$temp +=$plicand
}
$plier = halveValue$plier
$plicand = doubleValue$plicand
}

return $temp } multiplyValues 17 34  ### Pipes with Busywork This uses several PowerShell specific features, in functions everything is returned automatically, so explicitly stating return is unnecessary. type conversion happens automatically for certain types, [int] into [boolean] maps 0 to false and everything else to true. A hash is used to store the values as they are being written, then a pipeline is used to iterate over the keys of the hash, determine which are odd, and only sum those. The three-valued ForEach-Object is used to set a start expression, an iterative expression, and a return expression. function halveInt( [int]$rhs )
{
[math]::floor( $rhs / 2 ) } function doubleInt( [int]$rhs )
{
$rhs*2 } function isEven( [int]$rhs )
{
-not ( $_ % 2 ) } function Ethiopian( [int]$lhs , [int] $rhs ) {$scratch = @{}
1..[math]::floor( [math]::log( $lhs , 2 ) + 1 ) | ForEach-Object {$scratch[$lhs] =$rhs
$lhs$lhs = halveInt( $lhs )$rhs = doubleInt( $rhs ) } | Where-Object { -not ( isEven$_ ) } |
ForEach-Object { $sum = 0 } {$sum += $scratch[$_] } { $sum } } Ethiopian 17 34  ## Prolog ### Traditional halve(X,Y) :- Y is X // 2. double(X,Y) :- Y is 2*X. is_even(X) :- 0 is X mod 2. % columns(First,Second,Left,Right) is true if integers First and Second % expand into the columns Left and Right, respectively columns(1,Second,[1],[Second]). columns(First,Second,[First|Left],[Second|Right]) :- halve(First,Halved), double(Second,Doubled), columns(Halved,Doubled,Left,Right). % contribution(Left,Right,Amount) is true if integers Left and Right, % from their respective columns contribute Amount to the final sum. contribution(Left,_Right,0) :- is_even(Left). contribution(Left,Right,Right) :- \+ is_even(Left). ethiopian(First,Second,Product) :- columns(First,Second,Left,Right), maplist(contribution,Left,Right,Contributions), sumlist(Contributions,Product).  ### Functional Style Using the same definitions as above for "halve/2", "double/2" and "is_even/2" along with an SWI-Prolog pack for function notation, one might write the following solution :- use_module(library(func)). % halve/2, double/2, is_even/2 definitions go here ethiopian(First,Second,Product) :- ethiopian(First,Second,0,Product). ethiopian(1,Second,Sum0,Sum) :- Sum is Sum0 + Second. ethiopian(First,Second,Sum0,Sum) :- Sum1 is Sum0 + Second*(First mod 2), ethiopian(halve$ First, double $Second, Sum1, Sum).  ### Constraint Handling Rules This is a CHR solution for this problem using Prolog as the host language. Code will work in SWI-Prolog and YAP (and possibly in others with or without some minor tweaking). :- module(ethiopia, [test/0, mul/3]). :- use_module(library(chr)). :- chr_constraint mul/3, halve/2, double/2, even/1, add_odd/4. mul(1, Y, S) <=> S = Y. mul(X, Y, S) <=> X \= 1 | halve(X, X1), double(Y, Y1), mul(X1, Y1, S1), add_odd(X, Y, S1, S). halve(X, Y) <=> Y is X // 2. double(X, Y) <=> Y is X * 2. even(X) <=> 0 is X mod 2 | true. even(X) <=> 1 is X mod 2 | false. add_odd(X, _, A, S) <=> even(X) | S is A. add_odd(X, Y, A, S) <=> \+ even(X) | S is A + Y. test :- mul(17, 34, Z), !, writeln(Z).  Note that the task statement is what makes the halve and double constraints required. Their use is highly artificial and a more realistic implementation would look like this: :- module(ethiopia, [test/0, mul/3]). :- use_module(library(chr)). :- chr_constraint mul/3, even/1, add_if_odd/4. mul(1, Y, S) <=> S = Y. mul(X, Y, S) <=> X \= 1 | X1 is X // 2, Y1 is Y * 2, mul(X1, Y1, S1), add_if_odd(X, Y, S1, S). even(X) <=> 0 is X mod 2 | true. even(X) <=> 1 is X mod 2 | false. add_if_odd(X, _, A, S) <=> even(X) | S is A. add_if_odd(X, Y, A, S) <=> \+ even(X) | S is A + Y. test :- mul(17, 34, Z), writeln(Z).  Even this is more verbose than what a more native solution would look like. ## Python ### Python: With tutor tutor = True def halve(x): return x // 2 def double(x): return x * 2 def even(x): return not x % 2 def ethiopian(multiplier, multiplicand): if tutor: print("Ethiopian multiplication of %i and %i" % (multiplier, multiplicand)) result = 0 while multiplier >= 1: if even(multiplier): if tutor: print("%4i %6i STRUCK" % (multiplier, multiplicand)) else: if tutor: print("%4i %6i KEPT" % (multiplier, multiplicand)) result += multiplicand multiplier = halve(multiplier) multiplicand = double(multiplicand) if tutor: print() return result  Sample output Python 3.1 (r31:73574, Jun 26 2009, 20:21:35) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> ethiopian(17, 34) Ethiopian multiplication of 17 and 34 17 34 KEPT 8 68 STRUCK 4 136 STRUCK 2 272 STRUCK 1 544 KEPT 578 >>> ### Python: Without tutor Without the tutorial code, and taking advantage of Python's lambda: halve = lambda x: x // 2 double = lambda x: x*2 even = lambda x: not x % 2 def ethiopian(multiplier, multiplicand): result = 0 while multiplier >= 1: if not even(multiplier): result += multiplicand multiplier = halve(multiplier) multiplicand = double(multiplicand) return result  ### Python: With tutor. More Functional Using some features which Python has for use in functional programming. The example also tries to show how to mix different programming styles while keeping close to the task specification, a kind of "executable pseudocode". Note: While column2 could theoretically generate a sequence of infinite length, izip will stop requesting values from it (and so provide the necessary stop condition) when column1 has no more values. When not using the tutor, table will generate the table on the fly in an efficient way, not keeping any intermediate values. tutor = True from itertools import izip, takewhile def iterate(function, arg): while 1: yield arg arg = function(arg) def halve(x): return x // 2 def double(x): return x * 2 def even(x): return x % 2 == 0 def show_heading(multiplier, multiplicand): print "Multiplying %d by %d" % (multiplier, multiplicand), print "using Ethiopian multiplication:" print TABLE_FORMAT = "%8s %8s %8s %8s %8s" def show_table(table): for p, q in table: print TABLE_FORMAT % (p, q, "->", p, q if not even(p) else "-" * len(str(q))) def show_result(result): print TABLE_FORMAT % ('', '', '', '', "=" * (len(str(result)) + 1)) print TABLE_FORMAT % ('', '', '', '', result) def ethiopian(multiplier, multiplicand): def column1(x): return takewhile(lambda v: v >= 1, iterate(halve, x)) def column2(x): return iterate(double, x) def rows(x, y): return izip(column1(x), column2(y)) table = rows(multiplier, multiplicand) if tutor: table = list(table) show_heading(multiplier, multiplicand) show_table(table) result = sum(q for p, q in table if not even(p)) if tutor: show_result(result) return result  Example output: >>> ethiopian(17, 34) Multiplying 17 by 34 using Ethiopian multiplication:   17 34 -> 17 34 8 68 -> 8 -- 4 136 -> 4 --- 2 272 -> 2 --- 1 544 -> 1 544 ==== 578 578  ### Python: as an unfold followed by a fold Translation of: Haskell Works with: Python version 3.7 Avoiding the use of the multiplication operator, and defining a catamorphism applied over an anamorphism. '''Ethiopian multiplication''' from functools import reduce # ethMult :: Int -> Int -> Int def ethMult(n): '''Ethiopian multiplication of n by m.''' def doubled(x): return x + x def halved(h): qr = divmod(h, 2) if 0 < h: print('halve:', str(qr).rjust(8, ' ')) return qr if 0 < h else None def addedWhereOdd(a, remx): odd, x = remx if odd: print( str(a).rjust(2, ' '), '+', str(x).rjust(3, ' '), '->', str(a + x).rjust(3, ' ') ) return a + x else: print(str(x).rjust(8, ' ')) return a return lambda m: reduce( addedWhereOdd, zip( unfoldr(halved)(n), iterate(doubled)(m) ), 0 ) # ------------------------- TEST ------------------------- def main(): '''Tests of multiplication.''' print( '\nProduct: ' + str( ethMult(17)(34) ), '\n_______________\n' ) print( '\nProduct: ' + str( ethMult(34)(17) ) ) # ----------------------- GENERIC ------------------------ # iterate :: (a -> a) -> a -> Gen [a] def iterate(f): '''An infinite list of repeated applications of f to x. ''' def go(x): v = x while True: yield v v = f(v) return go # showLog :: a -> IO String def showLog(*s): '''Arguments printed with intercalated arrows.''' print( ' -> '.join(map(str, s)) ) # unfoldr :: (b -> Maybe (a, b)) -> b -> [a] def unfoldr(f): '''Dual to reduce or foldr. Where catamorphism reduces a list to a summary value, the anamorphic unfoldr builds a list from a seed value. As long as f returns Just(a, b), a is prepended to the list, and the residual b is used as the argument for the next application of f. When f returns Nothing, the completed list is returned.''' def go(v): xr = v, v xs = [] while True: xr = f(xr[0]) if xr: xs.append(xr[1]) else: return xs return xs return go # MAIN --- if __name__ == '__main__': main()  Output: halve: (8, 1) halve: (4, 0) halve: (2, 0) halve: (1, 0) halve: (0, 1) 0 + 34 -> 34 68 136 272 34 + 544 -> 578 Product: 578 _______________ halve: (17, 0) halve: (8, 1) halve: (4, 0) halve: (2, 0) halve: (1, 0) halve: (0, 1) 17 0 + 34 -> 34 68 136 272 34 + 544 -> 578 Product: 578 ## Quackery Translation of: Forth Extended to handle negative numbers. [ 1 & not ] is even ( n --> b ) [ 1 << ] is double ( n --> n ) [ 1 >> ] is halve ( n --> n ) [ dup 0 < unrot abs [ dup 0 = iff nip done over double over halve recurse swap even iff nip else + ] swap if negate ] is e* ( n n --> n ) ## R ### R: With tutor halve <- function(a) floor(a/2) double <- function(a) a*2 iseven <- function(a) (a%%2)==0 ethiopicmult <- function(plier, plicand, tutor=FALSE) { if (tutor) { cat("ethiopic multiplication of", plier, "and", plicand, "\n") } result <- 0 while(plier >= 1) { if (!iseven(plier)) { result <- result + plicand } if (tutor) { cat(plier, ", ", plicand, " ", ifelse(iseven(plier), "struck", "kept"), "\n", sep="") } plier <- halve(plier) plicand <- double(plicand) } result } print(ethiopicmult(17, 34, TRUE))  ### R: Without tutor Simplified version. halve <- function(a) floor(a/2) double <- function(a) a*2 iseven <- function(a) (a%%2)==0 ethiopicmult<-function(x,y){ res<-ifelse(iseven(y),0,x) while(!y==1){ x<-double(x) y<-halve(y) if(!iseven(y)) res<-res+x } return(res) } print(ethiopicmult(17,34))  ## Racket #lang racket (define (halve i) (quotient i 2)) (define (double i) (* i 2)) ;; even?' is built-in (define (ethiopian-multiply x y) (cond [(zero? x) 0] [(even? x) (ethiopian-multiply (halve x) (double y))] [else (+ y (ethiopian-multiply (halve x) (double y)))])) (ethiopian-multiply 17 34) ; -> 578  ## Raku (formerly Perl 6) sub halve (Int$n is rw)    { $n div= 2 } sub double (Int$n is rw)    { $n *= 2 } sub even (Int$n --> Bool) { $n %% 2 } sub ethiopic-mult (Int$a is copy, Int $b is copy --> Int) { my Int$r = 0;
while $a { even$a or $r +=$b;
halve $a; double$b;
}
return $r; } say ethiopic-mult(17,34);  Output: 578  More succinctly using implicit typing, primed lambdas, and an infinite loop: sub ethiopic-mult { my &halve = * div= 2; my &double = * *= 2; my &even = * %% 2; my ($a,$b) = @_; my$r;
loop {
even  $a or$r += $b; halve$a or return $r; double$b;
}
}

say ethiopic-mult(17,34);


More succinctly still, using a pure functional approach (reductions, mappings, lazy infinite sequences):

sub halve  { $^n div 2 } sub double {$^n * 2   }
sub even   { $^n %% 2 } sub ethiopic-mult ($a, $b) { [+] ($b, &double ... *)
Z*
($a, &halve ... 0).map: { not even$^n }
}

say ethiopic-mult(17,34);

(same output)

## Rascal

import IO;

public int halve(int n) = n/2;

public int double(int n) = n*2;

public bool uneven(int n) = (n % 2) != 0);

public int ethiopianMul(int n, int m) {
result = 0;
while(n >= 1) {
if(uneven(n))
result += m;
n = halve(n);
m = double(m);
}
return result;
}

## Red

Red["Ethiopian multiplication"]

halve: function [n][n >> 1]
double: function [n][n << 1]
;== even? already exists

ethiopian-multiply: function [
"Returns the product of two integers using Ethiopian multiplication"
a [integer!] "The multiplicand"
b [integer!] "The multiplier"
][
result: 0
while [a <> 0][
if odd? a [result: result + b]
a: halve a
b: double b
]
result
]

print ethiopian-multiply 17 34

Output:
578


## Relation

function half(x)
set result = floor(x/2)
end function

function double(x)
set result = 2*x
end function

function even(x)
set result = (x/2 > floor(x/2))
end function

program ethiopian_mul(a,b)
relation first, second
while a >= 1
insert a, b
set a = half(a)
set b = double(b)
end while
extend third = even(first) *  second
project third sum
end program

run ethiopian_mul(17,34)
print

## REXX

These two REXX versions properly handle negative integers.

### sans error checking

/*REXX program multiplies two integers by the  Ethiopian  (or Russian peasant)  method. */
numeric digits 3000                              /*handle some gihugeic integers.       */
parse arg a b .                                  /*get two numbers from the command line*/
say  'a=' a                                      /*display a formatted value of  A.     */
say  'b='   b                                    /*   "    "     "       "    "  B.     */
say  'product='    eMult(a, b)                   /*invoke eMult & multiple two integers.*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
eMult:   procedure;  parse arg x,y;  s=sign(x)   /*obtain the two arguments; sign for X.*/
$=0 /*product of the two integers (so far).*/ do while x\==0 /*keep processing while X not zero.*/ if \isEven(x) then$=$+y /*if odd, then add Y to product. */ x= halve(x) /*invoke the HALVE function. */ y=double(y) /* " " DOUBLE " */ end /*while*/ /* [↑] Ethiopian multiplication method*/ return$*s/1                            /*maintain the correct sign for product*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
double:  return  arg(1)  * 2                     /*   *   is REXX's  multiplication.    */
halve:   return  arg(1)  % 2                     /*   %    "   "     integer division.  */
isEven:  return  arg(1) // 2 == 0                /*   //   "   "     division remainder.*/

output   when the following input is used:   30   -7

a= 30
b= -7
product= -210


### with error checking

This REXX version also aligns the "input" messages and also performs some basic error checking.

Note that the 2nd number needn't be an integer, any valid number will work.

/*REXX program multiplies two integers by the  Ethiopian  (or Russian peasant)  method. */
numeric digits 3000                              /*handle some gihugeic integers.       */
parse arg a b _ .                                /*get two numbers from the command line*/
if a==''              then call error  "1st argument wasn't specified."
if b==''              then call error  "2nd argument wasn't specified."
if _\==''             then call error  "too many arguments were specified: "  _
if \datatype(a, 'W')  then call error  "1st argument isn't an integer: "      a
if \datatype(b, 'N')  then call error  "2nd argument isn't a valid number: "  b
p=eMult(a, b)                                    /*Ethiopian or Russian peasant method. */
w=max(length(a), length(b), length(p))           /*find the maximum width of 3 numbers. */
say  '      a='  right(a, w)                     /*use right justification to display A.*/
say  '      b='  right(b, w)                     /* "    "         "        "    "    B.*/
say  'product='  right(p, w)                     /* "    "         "        "    "    P.*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
eMult:   procedure;  parse arg x,y;  s=sign(x)   /*obtain the two arguments; sign for X.*/
$=0 /*product of the two integers (so far).*/ do while x\==0 /*keep processing while X not zero.*/ if \isEven(x) then$=$+y /*if odd, then add Y to product. */ x= halve(x) /*invoke the HALVE function. */ y=double(y) /* " " DOUBLE " */ end /*while*/ /* [↑] Ethiopian multiplication method*/ return$*s/1                            /*maintain the correct sign for product*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
double:  return  arg(1)  * 2                     /*   *   is REXX's  multiplication.    */
halve:   return  arg(1)  % 2                     /*   %    "   "     integer division.  */
isEven:  return  arg(1) // 2 == 0                /*   //   "   "     division remainder.*/
error:   say '***error!***' arg(1);    exit 13   /*display an error message to terminal.*/

output   when the following input is used:   200   0.333

      a=   200
b= 0.333
product=  66.6


## Ring

x = 17
y = 34
p = 0
while x != 0
if not even(x)
p += y
see "" + x + " " + " " + y + nl
else
see "" + x + "  ---" + nl ok
x = halve(x)
y = double(y)
end
see " " + "  ===" + nl
see "   " + p

func double n return (n * 2)
func halve n return floor(n / 2)
func even n return ((n & 1) = 0)

Output:

17  34
8  ---
4  ---
2  ---
1  544
===
578


## RPL

Calculations are here made on binary integers, on which built-in instructions SL and SR perform resp. doubling and halving.

Works with: Halcyon Calc version 4.2.7
RPL code Comment
≪ # 1d AND # 0d ==
≫ 'EVEN?' STO

≪
# 0d ROT R→B ROT R→B
WHILE OVER # 0d ≠ REPEAT
IF OVER EVEN? NOT
THEN ROT OVER + ROT ROT END
SL SWAP SR SWAP
END DROP2 B→R
≫ 'ETMUL' STO

EVEN? ( #n -- boolean )
return 1 if n is even, 0 otherwise

ETMUL ( a b  -- a*b )
put accumulator, a and b (converted to integers) in stack
while b > 0
if b is odd
add a to accumulator
double a, halve b
delete a and b and convert a*b to floating point



## Ruby

Iterative and recursive implementations here. I've chosen to highlight the example 20*5 which I think is more illustrative.

def halve(x) = x/2
def double(x) = x*2

# iterative
def ethiopian_multiply(a, b)
product = 0
while a >= 1
p [a, b, a.even? ? "STRIKE" : "KEEP"] if $DEBUG product += b unless a.even? a = halve(a) b = double(b) end product end # recursive def rec_ethiopian_multiply(a, b) return 0 if a < 1 p [a, b, a.even? ? "STRIKE" : "KEEP"] if$DEBUG
(a.even? ? 0 : b) + rec_ethiopian_multiply(halve(a), double(b))
end

$DEBUG = true #$DEBUG also set to true if "-d" option given
a, b = 20, 5
puts "#{a} * #{b} = #{ethiopian_multiply(a,b)}"; puts
Output:
[20, 5, "STRIKE"]
[10, 10, "STRIKE"]
[5, 20, "KEEP"]
[2, 40, "STRIKE"]
[1, 80, "KEEP"]
20 * 5 = 100

A test suite:

require 'test/unit'
class EthiopianTests < Test::Unit::TestCase
def test_iter1; assert_equal(578, ethopian_multiply(17,34)); end
def test_iter2; assert_equal(100, ethopian_multiply(20,5));  end
def test_iter3; assert_equal(5,   ethopian_multiply(5,1));   end
def test_iter4; assert_equal(5,   ethopian_multiply(1,5));   end
def test_iter5; assert_equal(0,   ethopian_multiply(5,0));   end
def test_iter6; assert_equal(0,   ethopian_multiply(0,5));   end
def test_rec1;  assert_equal(578, rec_ethopian_multiply(17,34)); end
def test_rec2;  assert_equal(100, rec_ethopian_multiply(20,5));  end
def test_rec3;  assert_equal(5,   rec_ethopian_multiply(5,1));   end
def test_rec4;  assert_equal(5,   rec_ethopian_multiply(1,5));   end
def test_rec5;  assert_equal(0,   rec_ethopian_multiply(5,0));   end
def test_rec6;  assert_equal(0,   rec_ethopian_multiply(0,5));   end
end
Run options:

# Running tests:

............
Finished tests in 0.014001s, 857.0816 tests/s, 857.0816 assertions/s.

12 tests, 12 assertions, 0 failures, 0 errors, 0 skips

ruby -v: ruby 2.0.0p247 (2013-06-27) [i386-mingw32]


## Rust

fn double(a: i32) -> i32 {
2*a
}

fn halve(a: i32) -> i32 {
a/2
}

fn is_even(a: i32) -> bool {
a % 2 == 0
}

fn ethiopian_multiplication(mut x: i32, mut y: i32) -> i32 {
let mut sum = 0;

while x >= 1 {
print!("{} \t {}", x, y);
match is_even(x) {
true  => println!("\t Not Kept"),
false => {
println!("\t Kept");
sum += y;
}
}
x = halve(x);
y = double(y);
}
sum
}

fn main() {
let output = ethiopian_multiplication(17, 34);
println!("---------------------------------");
println!("\t {}", output);
}
Output:
17       34      Kept
8        68      Not Kept
4        136     Not Kept
2        272     Not Kept
1        544     Kept
---------------------------------
578

## S-BASIC

$constant true = 0FFFFH$constant false =  0

function half(n = integer) = integer
end = n / 2

function twice(n = integer) = integer
end = n + n

rem - return true (-1) if n is even, otherwise false
function even(n = integer) = integer
var one = integer
one = 1   rem - only variables are compared bitwise
end = ((n and one) = 0)

rem - return i * j, optionally showing steps
function ethiopian(i, j, show = integer) = integer
var p = integer
p = 0
while i >= 1 do
begin
if even(i) then
begin
if show then print i;" ---";j
end
else
begin
if show then print i;"    ";j;"+"
p = p + j
end
i = half(i)
j = twice(j)
end
if show then
begin
print "----------"
print "     =";
end
end = p

rem - exercise the function
print "Multiplying 17 times 34"
print ethiopian(17,34,true)

end
Output:
Multiplying 17 times 34
17     34+
8 --- 68
4 --- 136
2 --- 272
1     544+
----------
= 578

## Scala

The first and second are only slightly different and use functional style. The third uses a for loop to yield the result. The fourth uses recursion.

def ethiopian(i:Int, j:Int):Int=
pairIterator(i,j).filter(x=> !isEven(x._1)).map(x=>x._2).foldLeft(0){(x,y)=>x+y}

def ethiopian2(i:Int, j:Int):Int=
pairIterator(i,j).map(x=>if(isEven(x._1)) 0 else x._2).foldLeft(0){(x,y)=>x+y}

def ethiopian3(i:Int, j:Int):Int=
{
var res=0;
for((h,d) <- pairIterator(i,j) if !isEven(h)) res+=d;
res
}

def ethiopian4(i: Int, j: Int): Int = if (i == 1) j else ethiopian(halve(i), double(j)) + (if (isEven(i)) 0 else j)

def isEven(x:Int)=(x&1)==0
def halve(x:Int)=x>>>1
def double(x:Int)=x<<1

// generates pairs of values (halve,double)
def pairIterator(x:Int, y:Int)=new Iterator[(Int, Int)]
{
var i=(x, y)
def hasNext=i._1>0
def next={val r=i; i=(halve(i._1), double(i._2)); r}
}

## Scheme

In Scheme, even? is a standard procedure.

(define (halve num)
(quotient num 2))

(define (double num)
(* num 2))

(define (*mul-eth plier plicand acc)
(cond ((zero? plier) acc)
((even? plier) (*mul-eth (halve plier) (double plicand) acc))
(else (*mul-eth (halve plier) (double plicand) (+ acc plicand)))))

(define (mul-eth plier plicand)
(*mul-eth plier plicand 0))

(display (mul-eth 17 34))
(newline)

Output:

578


## Seed7

Ethiopian Multiplication is another name for the peasant multiplication:

const proc: double (inout integer: a) is func
begin
a *:= 2;
end func;

const proc: halve (inout integer: a) is func
begin
a := a div 2;
end func;

const func boolean: even (in integer: a) is
return not odd(a);

const func integer: peasantMult (in var integer: a, in var integer: b) is func
result
var integer: result is 0;
begin
while a <> 0 do
if not even(a) then
result +:= b;
end if;
halve(a);
double(b);
end while;
end func;

Original source (without separate functions for doubling, halving, and checking if a number is even): [2]

## Sidef

func double (n) { n << 1 }
func halve  (n) { n >> 1 }
func isEven (n) { n&1 == 0 }

func ethiopian_mult(a, b) {
var r = 0
while (a > 0) {
r += b if !isEven(a)
a = halve(a)
b = double(b)
}
return r
}

say ethiopian_mult(17, 34)
Output:
578


## Smalltalk

Works with: GNU Smalltalk
Number extend [
double [ ^ self * 2 ]
halve  [ ^ self // 2 ]
ethiopianMultiplyBy: aNumber withTutor: tutor [
|result multiplier multiplicand|
multiplier := self.
multiplicand := aNumber.
tutor ifTrue: [ ('ethiopian multiplication of %1 and %2' %
{ multiplier. multiplicand }) displayNl ].
result := 0.
[ multiplier >= 1 ]
whileTrue: [
multiplier even ifFalse: [
result := result + multiplicand.
tutor ifTrue: [
('%1, %2 kept' % { multiplier. multiplicand })
displayNl
]
]
ifTrue: [
tutor ifTrue: [
('%1, %2 struck' % { multiplier. multiplicand })
displayNl
]
].
multiplier := multiplier halve.
multiplicand := multiplicand double.
].
^result
]
ethiopianMultiplyBy: aNumber [ ^ self ethiopianMultiplyBy: aNumber withTutor: false ]
].
(17 ethiopianMultiplyBy: 34 withTutor: true) displayNl.

## SNOBOL4

	define('halve(num)')	:(halve_end)
halve	eq(num,1)	:s(freturn)
halve = num / 2	:(return)
halve_end

define('double(num)')	:(double_end)
double	double = num * 2	:(return)
double_end

define('odd(num)')	:(odd_end)
odd	eq(num,1)	:s(return)
eq(num,double(halve(num)))	:s(freturn)f(return)

odd_end	l = trim(input)
r = trim(input)
s = 0
next	s = odd(l) s + r
r = double(r)
l = halve(l)	:s(next)
stop  	output = s
end

## SNUSP

    /==!/==atoi==@@@-@-----#
|   |          /-\          /recurse\    #/?\ zero
$>,@/>,@/?\<=zero=!\?/<=print==!\@\>?!\@/<@\.!\-/ < @ # | \=/ \=itoa=@@@+@+++++# /==\ \===?!/===-?\>>+# halve ! /+ !/+ !/+ !/+ \ mod10 # ! @ | #>>\?-<+>/ /<+> -\!?-\!?-\!?-\!?-\! /-<+>\ > ? />+<<++>-\ \?!\-?!\-?!\-?!\-?!\-?/\ div10 ?down? | \-<<<!\=======?/\ add & # +/! +/! +/! +/! +/ \>+<-/ | \=<<<!/====?\=\ | double ! # | \<++>-/ | | \=======\!@>============/!/ This is possibly the smallest multiply routine so far discovered for SNUSP. ## Soar ########################################## # multiply takes ^left and ^right numbers # and a ^return-to sp {multiply*elaborate*initialize (state <s> ^superstate.operator <o>) (<o> ^name multiply ^left <x> ^right <y> ^return-to <r>) --> (<s> ^name multiply ^left <x> ^right <y> ^return-to <r>)} sp {multiply*propose*recurse (state <s> ^name multiply ^left <x> > 0 ^right <y> ^return-to <r> -^multiply-done) --> (<s> ^operator <o> +) (<o> ^name multiply ^left (div <x> 2) ^right (* <y> 2) ^return-to <s>)} sp {multiply*elaborate*mod (state <s> ^name multiply ^left <x>) --> (<s> ^left-mod-2 (mod <x> 2))} sp {multiply*elaborate*recursion-done-even (state <s> ^name multiply ^left <x> ^right <y> ^multiply-done <temp> ^left-mod-2 0) --> (<s> ^answer <temp>)} sp {multiply*elaborate*recursion-done-odd (state <s> ^name multiply ^left <x> ^right <y> ^multiply-done <temp> ^left-mod-2 1) --> (<s> ^answer (+ <temp> <y>))} sp {multiply*elaborate*zero (state <s> ^name multiply ^left 0) --> (<s> ^answer 0)} sp {multiply*elaborate*done (state <s> ^name multiply ^return-to <r> ^answer <a>) --> (<r> ^multiply-done <a>)} ## Swift import Darwin func ethiopian(var #int1:Int, var #int2:Int) -> Int { var lhs = [int1], rhs = [int2] func isEven(#n:Int) -> Bool {return n % 2 == 0} func double(#n:Int) -> Int {return n * 2} func halve(#n:Int) -> Int {return n / 2} while int1 != 1 { lhs.append(halve(n: int1)) rhs.append(double(n: int2)) int1 = halve(n: int1) int2 = double(n: int2) } var returnInt = 0 for (a,b) in zip(lhs, rhs) { if (!isEven(n: a)) { returnInt += b } } return returnInt } println(ethiopian(int1: 17, int2: 34)) Output: 578 ## Tcl # This is how to declare functions - the mathematical entities - as opposed to procedures proc function {name arguments body} { uplevel 1 [list proc tcl::mathfunc::$name $arguments [list expr$body]]
}

function double n {$n * 2} function halve n {$n / 2}
function even n {($n & 1) == 0} function mult {a b} {$a < 1 ? 0 :
even($a) ? [logmult STRUCK] + mult(halve($a), double($b)) : [logmult KEPT] + mult(halve($a), double($b)) +$b
}

# Wrapper to set up the logging
proc ethiopianMultiply {a b {tutor false}} {
if {$tutor} { set wa [expr {[string length$a]+1}]
set wb [expr {$wa+[string length$b]-1}]
puts stderr "Ethiopian multiplication of $a and$b"
interp alias {} logmult {} apply {{wa wb msg} {
upvar 1 a a b b
puts stderr [format "%*d %*d %s" $wa$a $wb$b $msg] return 0 }}$wa $wb } else { proc logmult args {return 0} } return [expr {mult($a,$b)}] } Demo code: puts "17 * 34 = [ethiopianMultiply 17 34 true]" Output: Ethiopian multiplication of 17 and 34 17 34 KEPT 8 68 STRUCK 4 136 STRUCK 2 272 STRUCK 1 544 KEPT 17 * 34 = 578  ## TUSCRIPT $$MODE TUSCRIPT ASK "insert number1", nr1="" ASK "insert number2", nr2="" SET nrs=APPEND(nr1,nr2),size_nrs=SIZE(nrs) IF (size_nrs!=2) ERROR/STOP "insert two numbers" LOOP n=nrs IF (n!='digits') ERROR/STOP n, " is not a digit" ENDLOOP PRINT "ethopian multiplication of ",nr1," and ",nr2 SET sum=0 SECTION checkifeven SET even=MOD(nr1,2) IF (even==0) THEN SET action="struck" ELSE SET action="kept" SET sum=APPEND (sum,nr2) ENDIF SET nr1=CENTER (nr1,+6),nr2=CENTER (nr2,+6),action=CENTER (action,8) PRINT nr1,nr2,action ENDSECTION SECTION halve_i SET nr1=nr1/2 ENDSECTION SECTION double_i nr2=nr2*2 ENDSECTION DO checkifeven LOOP DO halve_i DO double_i DO checkifeven IF (nr1==1) EXIT ENDLOOP SET line=REPEAT ("=",20), sum = sum(sum),sum=CENTER (sum,+12) PRINT line PRINT sum Output: ethopian multiplication of 17 and 34 17 34 kept 8 68 struck 4 136 struck 2 272 struck 1 544 kept ==================== 578  ## TypeScript Translation of: Modula-2 // Ethiopian multiplication function double(a: number): number { return 2 * a; } function halve(a: number): number { return Math.floor(a / 2); } function isEven(a: number): bool { return a % 2 == 0; } function showEthiopianMultiplication(x: number, y: number): void { var tot = 0; while (x >= 1) { process.stdout.write(x.toString().padStart(9, ' ') + " "); if (!isEven(x)) { tot += y; process.stdout.write(y.toString().padStart(9, ' ')); } console.log(); x = halve(x); y = double(y); } console.log("=" + " ".repeat(9) + tot.toString().padStart(9, ' ')); } showEthiopianMultiplication(17, 34); Output:  17 34 8 4 2 1 544 = 578  ## UNIX Shell Tried with bash --posix, and also with Heirloom's sh. Beware that bash --posix has more features than sh; this script uses only sh features. Works with: Bourne Shell halve() { expr "$1" / 2
}

double()
{
expr "$1" \* 2 } is_even() { expr "$1" % 2 = 0 >/dev/null
}

ethiopicmult()
{
plier=$1 plicand=$2
r=0
while [ "$plier" -ge 1 ]; do is_even "$plier" || r=expr $r + "$plicand"
plier=halve "$plier" plicand=double "$plicand"
done
echo $r } ethiopicmult 17 34 # => 578 While breaking if the --posix flag is passed to bash, the following alternative script avoids the *, /, and % operators. It also uses local variables and built-in arithmetic. Works with: bash Works with: pdksh Works with: zsh halve() { (($1 >>= 1 ))
}

double() {
(( $1 <<= 1 )) } is_even() { (( ($1 & 1) == 0 ))
}

multiply() {
local plier=$1 local plicand=$2
local result=0

while (( plier > 0 ))
do
is_even plier || (( result += plicand ))
halve plier
double plicand
done
echo $result } multiply 17 34 # => 578 ### C Shell alias halve '@ \!:1 /= 2' alias double '@ \!:1 *= 2' alias is_even '@ \!:1 = ! ( \!:2 % 2 )' alias multiply eval \''set multiply_args=( \!*:q ) \\ @ multiply_plier =$multiply_args[2]			\\
@ multiply_plicand = $multiply_args[3] \\ @ multiply_result = 0 \\ while ($multiply_plier > 0 )				\\
is_even multiply_is_even $multiply_plier \\ if ( !$multiply_is_even ) then			\\
@ multiply_result += $multiply_plicand \\ endif \\ halve multiply_plier \\ double multiply_plicand \\ end \\ @$multiply_args[1] = $multiply_result \\ '\' multiply p 17 34 echo$p
# => 578

## Ursala

This solution makes use of the functions odd, double, and half, which respectively check the parity, double a given natural number, or perform truncating division by two. These functions are normally imported from the nat library but defined here explicitly for

the sake of completeness.
odd    = ~&ihB
double = ~&iNiCB
half   = ~&itB
The functions above are defined in terms of bit manipulations exploiting the concrete representations of natural numbers. The remaining code treats natural numbers instead as abstract types by way of the library API, and uses the operators for distribution (*-), triangular iteration (|\), and filtering (*~) among others.
#import nat

emul = sum:-0@rS+ odd@l*~+ ^|(~&,double)|\+ *-^|\~& @iNC ~&h~=0->tx :^/half@h ~&
test program:
#cast %n

test = emul(34,17)
Output:
578


## VBA

Define three named functions :

1. one to halve an integer,
2. one to double an integer, and
3. one to state if an integer is even.
Private Function lngHalve(Nb As Long) As Long
lngHalve = Nb / 2
End Function

Private Function lngDouble(Nb As Long) As Long
lngDouble = Nb * 2
End Function

Private Function IsEven(Nb As Long) As Boolean
IsEven = (Nb Mod 2 = 0)
End Function

Use these functions to create a function that does Ethiopian multiplication. The first function below is a non optimized function :

Private Function Ethiopian_Multiplication_Non_Optimized(First As Long, Second As Long) As Long
Dim Left_Hand_Column As New Collection, Right_Hand_Column As New Collection, i As Long, temp As Long

'Take two numbers to be multiplied and write them down at the top of two columns.
'In the left-hand column repeatedly halve the last number, discarding any remainders,
'and write the result below the last in the same column, until you write a value of 1.
Do
First = lngHalve(First)
Loop While First > 1
'In the right-hand column repeatedly double the last number and write the result below.
'stop when you add a result in the same row as where the left hand column shows 1.
For i = 2 To Left_Hand_Column.Count
Second = lngDouble(Second)
Next

'Examine the table produced and discard any row where the value in the left column is even.
For i = Left_Hand_Column.Count To 1 Step -1
If IsEven(Left_Hand_Column(i)) Then Right_Hand_Column.Remove CStr(Right_Hand_Column(i))
Next
'Sum the values in the right-hand column that remain to produce the result of multiplying
'the original two numbers together
For i = 1 To Right_Hand_Column.Count
temp = temp + Right_Hand_Column(i)
Next
Ethiopian_Multiplication_Non_Optimized = temp
End Function

This one is better :

Private Function Ethiopian_Multiplication(First As Long, Second As Long) As Long
Do
If Not IsEven(First) Then Mult_Eth = Mult_Eth + Second
First = lngHalve(First)
Second = lngDouble(Second)
Loop While First >= 1
Ethiopian_Multiplication = Mult_Eth
End Function

Then you can call one of these functions like this :

Sub Main_Ethiopian()
Dim result As Long
result = Ethiopian_Multiplication(17, 34)
' or :
'result = Ethiopian_Multiplication_Non_Optimized(17, 34)
Debug.Print result
End Sub

## VBScript

Nowhere near as optimal a solution as the Ada. Yes, it could have made as optimal, but the long way seemed more interesting.

Demonstrates a List class. The .recall and .replace methods have bounds checking but the code does not test for the exception that would be raised. List class extends the storage allocated for the list when the occupation of the list goes beyond the original allocation.

option explicit makes sure that all variables are declared.

Implementation
option explicit

class List
private theList
private nOccupiable
private nTop

sub class_initialize
nTop = 0
nOccupiable = 100
redim theList( nOccupiable )
end sub

public sub store( x )
if nTop >= nOccupiable then
nOccupiable = nOccupiable + 100
redim preserve theList( nOccupiable )
end if
theList( nTop ) = x
nTop = nTop + 1
end sub

public function recall( n )
if n >= 0 and n <= nOccupiable then
recall = theList( n )
else
err.raise vbObjectError + 1000,,"Recall bounds error"
end if
end function

public sub replace( n, x )
if n >= 0 and n <= nOccupiable then
theList( n )  = x
else
err.raise vbObjectError + 1001,,"Replace bounds error"
end if
end sub

public property get listCount
listCount = nTop
end property

end class

function halve( n )
halve = int( n / 2 )
end function

function twice( n )
twice = int( n * 2 )
end function

function iseven( n )
iseven = ( ( n mod 2 ) = 0 )
end function

function multiply( n1, n2 )
dim LL
set LL = new List

dim RR
set RR = new List

LL.store n1
RR.store n2

do while n1 <> 1
n1 = halve( n1 )
LL.store n1
n2 = twice( n2 )
RR.store n2
loop

dim i
for i = 0 to LL.listCount
if iseven( LL.recall( i ) ) then
RR.replace i, 0
end if
next

dim total
total = 0
for i = 0 to RR.listCount
total = total + RR.recall( i )
next

multiply = total
end function
Invocation
wscript.echo multiply(17,34)
Output:
578


## V (Vlang)

Translation of: go
fn halve(i int) int { return i/2 }

fn double(i int) int { return i*2 }

fn is_even(i int) bool { return i%2 == 0 }

fn eth_multi(ii int, jj int) int {
mut r := 0
mut i, mut j := ii, jj
for ; i > 0; i, j = halve(i), double(j) {
if !is_even(i) {
r += j
}
}
return r
}

fn main() {
println("17 ethiopian 34 = \${eth_multi(17, 34)}")
}
Output:
17 ethiopian 34 = 578

## Wren

var halve = Fn.new { |n| (n/2).truncate }

var double = Fn.new { |n| n * 2 }

var isEven = Fn.new { |n| n%2 == 0 }

var ethiopian = Fn.new { |x, y|
var sum = 0
while (x >= 1) {
if (!isEven.call(x)) sum = sum + y
x = halve.call(x)
y = double.call(y)
}
return sum
}

System.print("17 x 34 = %(ethiopian.call(17, 34))")
System.print("99 x 99 = %(ethiopian.call(99, 99))")
Output:
17 x 34 = 578
99 x 99 = 9801


## x86 Assembly

Works with: nasm
, linking with the C standard library and start code.
	extern 	printf
global	main

section	.text

halve
shr	ebx, 1
ret

double
shl	ebx, 1
ret

iseven
and	ebx, 1
cmp	ebx, 0
ret			; ret preserves flags

main
push	1		; tutor = true
push	34		; 2nd operand
push	17		; 1st operand
call	ethiopicmult

push	eax		; result of 17*34
push	fmt
call	printf

ret

%define plier 8
%define plicand 12
%define tutor 16

ethiopicmult
enter	0, 0
cmp	dword [ebp + tutor], 0
je	.notut0
push	dword [ebp + plicand]
push	dword [ebp + plier]
push	preamblefmt
call	printf
.notut0

xor	eax, eax		; eax -> result
mov	ecx, [ebp + plier] 	; ecx -> plier
mov	edx, [ebp + plicand]    ; edx -> plicand

.whileloop
cmp	ecx, 1
jl	.multend
cmp	dword [ebp + tutor], 0
je	.notut1
call	tutorme
.notut1
mov	ebx, ecx
call	iseven
je	.iseven
add	eax, edx	; result += plicand
.iseven
mov	ebx, ecx	; plier >>= 1
call	halve
mov	ecx, ebx

mov	ebx, edx	; plicand <<= 1
call	double
mov	edx, ebx

jmp	.whileloop
.multend
leave
ret

tutorme
push	eax
push	strucktxt
mov	ebx, ecx
call	iseven
je	.nostruck
mov	dword [esp], kepttxt
.nostruck
push	edx
push	ecx
push	tutorfmt
call	printf
pop	ecx
pop	edx
pop	eax
ret

section .data

fmt
db	"%d", 10, 0
preamblefmt
db	"ethiopic multiplication of %d and %d", 10, 0
tutorfmt
db	"%4d %6d %s", 10, 0
strucktxt
db	"struck", 0
kepttxt
db	"kept", 0

### Smaller version

Using old style 16 bit registers created in debug

The functions to halve double and even are coded inline. To half a value

  shr,1


to double a value

  shl,1


to test if the value is even

test,01
jz   Even
Odd:
Even:
;calling program

1BDC:0100 6A11           PUSH   11  ;17  Put operands on the stack
1BDC:0102 6A22           PUSH   22  ;34
1BDC:0104 E80900         CALL   0110  ; call the mulitplcation routine
;putting some space in, (not needed)
1BDC:0107 90             NOP
1BDC:0108 90             NOP
1BDC:0109 90             NOP
1BDC:010A 90             NOP
1BDC:010B 90             NOP
1BDC:010C 90             NOP
1BDC:010D 90             NOP
1BDC:010E 90             NOP
1BDC:010F 90             NOP
;mulitplication routine starts here
1BDC:0110 89E5           MOV    BP,SP      ; prepare to get operands off stack
1BDC:0112 8B4E02         MOV    CX,[BP+02] ; Get the first operand
1BDC:0115 8B5E04         MOV    BX,[BP+04] ; get the second oerand
1BDC:0118 31C0           XOR    AX,AX      ; zero out the result
1BDC:011A F7C10100       TEST   CX,0001     ; are we odd
1BDC:011E 7402           JZ     0122       ; no skip the next instruction
1BDC:0120 01D8           ADD    AX,BX     ; we are odd so add to the result
1BDC:0122 D1E3           SHL    BX,1      ; multiply by 2
1BDC:0124 D1E9           SHR    CX,1      ; divide by 2 (if zr flag is set, we are done)
1BDC:0126 75F2           JNZ    011A      ; cx not 0, go back and do it again
1BDC:0128 C3             RET              ; return with the result in AX

;pretty small, just 24 bytes

## XPL0

include c:\cxpl\codes;  \intrinsic 'code' declarations

func Halve(N);          \Return half of N
int  N;
return N>>1;

func Double(N);         \Return N doubled
int  N;
return N<<1;

func IsEven(N);         \Return 'true' if N is an even number
int  N;
return (N&1)=0;

func EthiopianMul(A, B); \Multiply A times B using Ethiopian method
int  A, B;
int  I, J, S, Left(100), Right(100);
[Left(0):= A;  Right(0):= B;            \1. write numbers to be multiplied
I:= 1;                                  \2. repeatedly halve number on left
repeat  A:= Halve(A);
Left(I):= A;  I:= I+1;
until   A=1;
J:= 1;                                  \3. repeatedly double number on right
repeat  B:= Double(B);
Right(J):= B;  J:= J+1;
until   J=I;                            \stop where left column = 1
for J:= 0 to I-1 do                     \4. discard right value if left is even
if IsEven(Left(J)) then Right(J):= 0;
S:= 0;                                  \5. sum remaining values on right
for J:= 0 to I-1 do
S:= S + Right(J);
for J:= 0 to I-1 do                     \show this insanity
[IntOut(0, Left(J));  ChOut(0, 9\tab\);  IntOut(0, Right(J));  CrLf(0)];
Text(0, "       --------
");
return S;                               \sum = product
];

int Product;
[Product:= EthiopianMul(17, 34);
ChOut(0, 9);  IntOut(0, Product);  CrLf(0);  CrLf(0);
Product:= EthiopianMul(1234, 5678);
ChOut(0, 9);  IntOut(0, Product);  CrLf(0);
]
Output:
17      34
8       0
4       0
2       0
1       544
--------
578

1234    0
617     11356
308     0
154     0
77      90848
38      0
19      363392
9       726784
4       0
2       0
1       5814272
--------
7006652

## zig

// programme multiplication ethiopienne
// Ethiopian multiplication

const std = @import("std");
const expect = std.testing.expect;
const print = @import("std").debug.print;

pub fn main() !void {
const Res = multiEth(17,34);
print("Resultat= {} \n", .{ Res });
}
test "Ethiopian multiplication" {
try expect(multiEth(20, 10) == 200);
try expect(multiEth(101, 101) == 10201);
try expect(multiEth(20, 0) == 0);
try expect(multiEth(0, 71) == 0);
}

//*****************************
// multiplication
//*****************************
fn multiEth(X: i64, Y: i64) i64 {
var X1=X;
var Y1=Y;
var sum: i64 = 0;
while (X1>=1) {
if ((@mod(X1,2)) == 1)
sum += Y1;
Y1= Y1 * 2;
X1 =  @divFloor(X1,2);
}

return sum;
}
Output:
Resultat= 578


## zkl

Trying to duplicate the task as stated, using columns. isEven is a integer method.

fcn ethiopianMultiply(l,r){ // l is a non-negative integer
halve  :=fcn(n){ n/2 };
double :=fcn(n){ n+n };
lr:=List(T(l,r)); // ( (l,r) .. (1,r*n) )
while(l>1){ lr.write( T(l=halve(l),r=double(r)) ) }
lr.filter(fcn([(l,r)]){ (not l.isEven) }); // strike out even left rows
.reduce(fcn(sum,[(l,r)]){ sum + r },0);  // sum right column
}
foreach l,r in ( T(T(17,34),T(34,1),T(34,2),T(34,0)) ){
println(ethiopianMultiply(l,r)," ",ethiopianMultiply(r,l));
}
Output:
578 578
34 34
68 68
0 0


## Z80 Assembly

	org &8000

ld hl,17
call Halve_Until_1

push bc
ld hl,34
call Double_Until_1
pop bc

call SumOddEntries
;returns Ethiopian product in IX.

call NewLine

call Primm
byte "0x",0

push ix
pop hl

ld a,H
call ShowHex
;Output should be in decimal but hex is easier.
ld a,L
call ShowHex

ret

Halve_Until_1:
;input: HL = number you wish to halve. HL is unsigned.
ld de,Column_1
ld a,1
ld (Column_1),HL
inc de
inc de
loop_HalveUntil_1:
SRL H
RR L
inc b
push af
ld a,L
ld (de),a
inc de
ld a,H
ld (de),a
inc de
pop af
CP L
jr nz,loop_HalveUntil_1
;b tracks how many times to double the second factor.
ret

Double_Until_1:
;doubles second factor B times. B is calculated by Halve_until_1
ld de,Column_2
ld (Column_2),HL
inc de
inc de
loop_double_until_1:
SLA L
RL H
PUSH AF
LD A,L
LD (DE),A
INC DE
LD A,H
LD (DE),A
INC DE
POP AF
DJNZ loop_double_until_1
ret

SumOddEntries:
sla b			;double loop counter, this is also the offset to the "last" entry of
;each table
ld h,>Column_1
ld d,>Column_2	;aligning the tables lets us get away with this.
ld l,b
ld e,b
ld ix,0
loop:
ld a,(hl)
rrca	;we only need the result of the odd/even test.
jr nc,skipEven
push hl
push de
ld a,(de)
ld L,a
inc de
ld a,(de)
ld H,a
ex de,hl
pop de
pop hl
skipEven:
dec de
dec de
dec hl
dec hl
djnz loop
ret	;ix should contain the answer

align 8		;aligns Column_1 to the nearest 256 byte boundary. This makes offsetting easier.
Column_1:
ds 16,0

align 8		;aligns Column_2 to the nearest 256 byte boundary. This makes offsetting easier.
Column_2:
ds 16,0
Output:

Output is in hex but is otherwise correct.

0x0242


## ZX Spectrum Basic

Translation of: GW-BASIC
10 DEF FN e(a)=a-INT (a/2)*2-1
20 DEF FN h(a)=INT (a/2)
30 DEF FN d(a)=2*a
40 LET x=17: LET y=34: LET tot=0
50 IF x<1 THEN GO TO 100
60 PRINT x;TAB (4);
70 IF FN e(x)=0 THEN LET tot=tot+y: PRINT y: GO TO 90
80 PRINT "---"
90 LET x=FN h(x): LET y=FN d(y): GO TO 50
100 PRINT TAB (4);"===",TAB (4);tot